Counts of unlabelled simple graphs. For each n, a table of values (edges, connected graphs, all graphs) is given. Computed using Maple by Brendan McKay with help from Gordon Royle. counts for n=1 0, 1, 1 totals: 1, 1 counts for n=2 0, 0, 1 1, 1, 1 totals: 1, 2 counts for n=3 0, 0, 1 1, 0, 1 2, 1, 1 3, 1, 1 totals: 2, 4 counts for n=4 0, 0, 1 1, 0, 1 2, 0, 2 3, 2, 3 4, 2, 2 5, 1, 1 6, 1, 1 totals: 6, 11 counts for n=5 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 4 4, 3, 6 5, 5, 6 6, 5, 6 7, 4, 4 8, 2, 2 9, 1, 1 10, 1, 1 totals: 21, 34 counts for n=6 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 9 5, 6, 15 6, 13, 21 7, 19, 24 8, 22, 24 9, 20, 21 10, 14, 15 11, 9, 9 12, 5, 5 13, 2, 2 14, 1, 1 15, 1, 1 totals: 112, 156 counts for n=7 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 10 5, 0, 21 6, 11, 41 7, 33, 65 8, 67, 97 9, 107, 131 10, 132, 148 11, 138, 148 12, 126, 131 13, 95, 97 14, 64, 65 15, 40, 41 16, 21, 21 17, 10, 10 18, 5, 5 19, 2, 2 20, 1, 1 21, 1, 1 totals: 853, 1044 counts for n=8 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 24 6, 0, 56 7, 23, 115 8, 89, 221 9, 236, 402 10, 486, 663 11, 814, 980 12, 1169, 1312 13, 1454, 1557 14, 1579, 1646 15, 1515, 1557 16, 1290, 1312 17, 970, 980 18, 658, 663 19, 400, 402 20, 220, 221 21, 114, 115 22, 56, 56 23, 24, 24 24, 11, 11 25, 5, 5 26, 2, 2 27, 1, 1 28, 1, 1 totals: 11117, 12346 counts for n=9 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 25 6, 0, 63 7, 0, 148 8, 47, 345 9, 240, 771 10, 797, 1637 11, 2075, 3252 12, 4495, 5995 13, 8404, 10120 14, 13855, 15615 15, 20303, 21933 16, 26631, 27987 17, 31400, 32403 18, 33366, 34040 19, 31996, 32403 20, 27764, 27987 21, 21817, 21933 22, 15558, 15615 23, 10096, 10120 24, 5984, 5995 25, 3247, 3252 26, 1635, 1637 27, 770, 771 28, 344, 345 29, 148, 148 30, 63, 63 31, 25, 25 32, 11, 11 33, 5, 5 34, 2, 2 35, 1, 1 36, 1, 1 totals: 261080, 274668 counts for n=10 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 66 7, 0, 165 8, 0, 428 9, 106, 1103 10, 657, 2769 11, 2678, 6759 12, 8548, 15772 13, 22950, 34663 14, 53863, 71318 15, 112618, 136433 16, 211866, 241577 17, 361342, 395166 18, 561106, 596191 19, 795630, 828728 20, 1032754, 1061159 21, 1229228, 1251389 22, 1343120, 1358852 23, 1348674, 1358852 24, 1245369, 1251389 25, 1057896, 1061159 26, 827086, 828728 27, 595418, 596191 28, 394820, 395166 29, 241428, 241577 30, 136370, 136433 31, 71293, 71318 32, 34652, 34663 33, 15767, 15772 34, 6757, 6759 35, 2768, 2769 36, 1102, 1103 37, 428, 428 38, 165, 165 39, 66, 66 40, 26, 26 41, 11, 11 42, 5, 5 43, 2, 2 44, 1, 1 45, 1, 1 totals: 11716571, 12005168 counts for n=11 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 67 7, 0, 172 8, 0, 467 9, 0, 1305 10, 235, 3664 11, 1806, 10250 12, 8833, 28259 13, 33851, 75415 14, 109844, 192788 15, 313670, 467807 16, 803905, 1069890 17, 1870168, 2295898 18, 3978187, 4609179 19, 7775398, 8640134 20, 14013042, 15108047 21, 23350556, 24630887 22, 36052412, 37433760 23, 51662585, 53037356 24, 68803769, 70065437 25, 85251441, 86318670 26, 98355794, 99187806 27, 105723785, 106321628 28, 105925685, 106321628 29, 98945882, 99187806 30, 86182087, 86318670 31, 69994055, 70065437 32, 53002668, 53037356 33, 37417977, 37433760 34, 24624123, 24630887 35, 15105276, 15108047 36, 8639030, 8640134 37, 4608750, 4609179 38, 2295733, 2295898 39, 1069824, 1069890 40, 467781, 467807 41, 192777, 192788 42, 75410, 75415 43, 28257, 28259 44, 10249, 10250 45, 3663, 3664 46, 1305, 1305 47, 467, 467 48, 172, 172 49, 67, 67 50, 26, 26 51, 11, 11 52, 5, 5 53, 2, 2 54, 1, 1 55, 1, 1 totals: 1006700565, 1018997864 counts for n=12 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 68 7, 0, 175 8, 0, 485 9, 0, 1405 10, 0, 4191 11, 551, 12763 12, 5026, 39243 13, 28908, 119890 14, 130365, 359307 15, 499888, 1043774 16, 1694642, 2911086 17, 5184582, 7739601 18, 14484609, 19515361 19, 37234106, 46505609 20, 88525650, 104504341 21, 195410521, 221147351 22, 401665379, 440393606 23, 770641945, 825075506 24, 1382812173, 1454265734 25, 2324370686, 2411961516 26, 3665000607, 3765262970 27, 5427096867, 5534255092 28, 7554423219, 7661345277 29, 9892755100, 9992340187 30, 12195279971, 12281841209 31, 14159301249, 14229503560 32, 15489241571, 15542350436 33, 15968704512, 16006173014 34, 15517703745, 15542350436 35, 14214388740, 14229503560 36, 12273198300, 12281841209 37, 9987729903, 9992340187 38, 7659048949, 7661345277 39, 5533185036, 5534255092 40, 3764795097, 3765262970 41, 2411768702, 2411961516 42, 1454190308, 1454265734 43, 825047242, 825075506 44, 440383354, 440393606 45, 221143686, 221147351 46, 104503035, 104504341 47, 46505142, 46505609 48, 19515189, 19515361 49, 7739534, 7739601 50, 2911060, 2911086 51, 1043763, 1043774 52, 359302, 359307 53, 119888, 119890 54, 39242, 39243 55, 12762, 12763 56, 4191, 4191 57, 1405, 1405 58, 485, 485 59, 175, 175 60, 68, 68 61, 26, 26 62, 11, 11 63, 5, 5 64, 2, 2 65, 1, 1 66, 1, 1 totals: 164059830476, 165091172592 counts for n=13 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 68 7, 0, 176 8, 0, 492 9, 0, 1446 10, 0, 4435 11, 0, 14140 12, 1301, 46415 13, 13999, 154658 14, 93569, 517121 15, 489387, 1711908 16, 2179949, 5546619 17, 8610789, 17422984 18, 30809058, 52664857 19, 101093020, 152339952 20, 306619793, 420048805 21, 864317147, 1101083128 22, 2273437235, 2739261020 23, 5597433239, 6461056816 24, 12932769342, 14441470390 25, 28100037365, 30583652956 26, 57519070110, 61372294334 27, 111089419502, 116724411757 28, 202705284331, 210474287115 29, 349854951952, 359954668522 30, 571708043354, 584089835857 31, 885315952770, 899632282299 32, 1300116617536, 1315729343451 33, 1811764113815, 1827823498798 34, 2397114478044, 2412694353115 35, 3012567495251, 3026821673656 36, 3597513119353, 3609810088490 37, 4083272448966, 4093273437761 38, 4406012122869, 4413678080790 39, 4520384306832, 4525920859198 40, 4409911747398, 4413678080790 41, 4090861008231, 4093273437761 42, 3608355629886, 3609810088490 43, 3025996522703, 3026821673656 44, 2412253931236, 2412694353115 45, 1827602341191, 1827823498798 46, 1315624835444, 1315729343451 47, 899585775383, 899632282299 48, 584070320028, 584089835857 49, 359946928749, 359954668522 50, 210471375962, 210474287115 51, 116723367957, 116724411757 52, 61371935016, 61372294334 53, 30583533061, 30583652956 54, 14441431145, 14441470390 55, 6461044052, 6461056816 56, 2739256828, 2739261020 57, 1101081723, 1101083128 58, 420048320, 420048805 59, 152339777, 152339952 60, 52664789, 52664857 61, 17422958, 17422984 62, 5546608, 5546619 63, 1711903, 1711908 64, 517119, 517121 65, 154657, 154658 66, 46414, 46415 67, 14140, 14140 68, 4435, 4435 69, 1446, 1446 70, 492, 492 71, 176, 176 72, 68, 68 73, 26, 26 74, 11, 11 75, 5, 5 76, 2, 2 77, 1, 1 78, 1, 1 totals: 50335907869219, 50502031367952 counts for n=14 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 68 7, 0, 177 8, 0, 495 9, 0, 1464 10, 0, 4541 11, 0, 14775 12, 0, 50159 13, 3159, 175652 14, 39260, 628635 15, 300748, 2271860 16, 1799700, 8191607 17, 9181185, 29148848 18, 41613518, 101403945 19, 171301235, 342260293 20, 648723984, 1114246152 21, 2278745633, 3483731123 22, 7466604072, 10428156463 23, 22916781627, 29823515196 24, 66099464855, 81379048741 25, 179638437584, 211701728866 26, 461011580013, 524838288774 27, 1119306632640, 1239859474951 28, 2575222889571, 2791316427401 29, 5622435575500, 5990156004406 30, 11663261941318, 12257461922574 31, 23013407529653, 23925444193310 32, 43234705737618, 44564782413424 33, 77402043968500, 79245514741538 34, 132152655846345, 134581443007315 35, 215327701580998, 218370131994476 36, 335032391116513, 338656477955759 37, 498043461420246, 502149047941551 38, 707689564672453, 712113254298926 39, 961585825489930, 966119418676935 40, 1249834675602570, 1254253893785795 41, 1554398715428131, 1558495757031738 42, 1850212617950038, 1853824841346885 43, 2108207254742072, 2111235531267396 44, 2299855868850890, 2302269388519749 45, 2402302590759788, 2404130854745735 46, 2402814904220039, 2404130854745735 47, 2301369651720480, 2302269388519749 48, 2110651394921418, 2111235531267396 49, 1853464867161397, 1853824841346885 50, 1558285275004448, 1558495757031738 51, 1254137166462738, 1254253893785795 52, 966058045338745, 966119418676935 53, 712082670286631, 712113254298926 54, 502134606351257, 502149047941551 55, 338650016859694, 338656477955759 56, 218367392720691, 218370131994476 57, 134580341919994, 134581443007315 58, 79245094691327, 79245514741538 59, 44564630072987, 44564782413424 60, 23925391528278, 23925444193310 61, 12257444499522, 12257461922574 62, 5990150457761, 5990156004406 63, 2791314715482, 2791316427401 64, 1239858957825, 1239859474951 65, 524838134114, 524838288774 66, 211701682450, 211701728866 67, 81379034600, 81379048741 68, 29823510761, 29823515196 69, 10428155017, 10428156463 70, 3483730631, 3483731123 71, 1114245976, 1114246152 72, 342260225, 342260293 73, 101403919, 101403945 74, 29148837, 29148848 75, 8191602, 8191607 76, 2271858, 2271860 77, 628634, 628635 78, 175651, 175652 79, 50159, 50159 80, 14775, 14775 81, 4541, 4541 82, 1464, 1464 83, 495, 495 84, 177, 177 85, 68, 68 86, 26, 26 87, 11, 11 88, 5, 5 89, 2, 2 90, 1, 1 91, 1, 1 totals: 29003487462848061, 29054155657235488 counts for n=15 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 68 7, 0, 177 8, 0, 496 9, 0, 1471 10, 0, 4583 11, 0, 15036 12, 0, 51814 13, 0, 185987 14, 7741, 691001 15, 110381, 2632420 16, 959374, 10176660 17, 6499706, 39500169 18, 37539466, 152374465 19, 192842712, 578891716 20, 901377310, 2149523582 21, 3885009655, 7753406889 22, 15572583105, 27040032015 23, 58393017190, 90859878747 24, 205715634053, 293429720936 25, 683177510788, 909199479603 26, 2144541235919, 2699941862354 27, 6377475240399, 7678976881470 28, 18001615191104, 20910536197366 29, 48311050541875, 54513628209893 30, 123449595358013, 136070590191317 31, 300749354421503, 325264684039708 32, 699350108423184, 744823014518211 33, 1553855733393286, 1634428386201309 34, 3301861994911062, 3438285431507061 35, 6715921394433155, 6936720574597423 36, 13085237079085229, 13426937977152944 37, 24439136746521945, 24944913304587039 38, 43781285251726544, 44497508446112065 39, 75271977853717106, 76242525660396354 40, 124262478451794760, 125521270445592815 41, 197063431080433042, 198626349980261157 42, 300336662510870107, 302194587531738164 43, 440052795351963640, 442167645425634116 44, 620062341104086439, 622367640359865212 45, 840472214620329758, 842878760010352632 46, 1096166036361399038, 1098571996084797125 47, 1375900185773096860, 1378203771448328912 48, 1662392479364026361, 1664504614806849040 49, 1933664512190616574, 1935518921253340732 50, 2165616006894383011, 2167174862664381524 51, 2335467291963665033, 2336721756356087856 52, 2425409960013204929, 2426376196165902704 53, 2425664021535713098, 2426376196165902704 54, 2336219576723209859, 2336721756356087856 55, 2166836191744515302, 2167174862664381524 56, 1935300544660143022, 1935518921253340732 57, 1664370030624532870, 1664504614806849040 58, 1378124524832488687, 1378203771448328912 59, 1098527430882329780, 1098571996084797125 60, 842854834413817653, 842878760010352632 61, 622355382845277188, 622367640359865212 62, 442161655252206509, 442167645425634116 63, 302191796209764061, 302194587531738164 64, 198625110119074266, 198626349980261157 65, 125520745606786906, 125521270445592815 66, 76242313958512824, 76242525660396354 67, 44497427067016907, 44497508446112065 68, 24944883481057701, 24944913304587039 69, 13426927548992045, 13426937977152944 70, 6936717090864854, 6936720574597423 71, 3438284317260417, 3438285431507061 72, 1634428043940840, 1634428386201309 73, 744822913114198, 744823014518211 74, 325264654890834, 325264684039708 75, 136070581999699, 136070590191317 76, 54513625938028, 54513628209893 77, 20910535568729, 20910536197366 78, 7678976705817, 7678976881470 79, 2699941812194, 2699941862354 80, 909199464828, 909199479603 81, 293429716395, 293429720936 82, 90859877283, 90859878747 83, 27040031520, 27040032015 84, 7753406712, 7753406889 85, 2149523514, 2149523582 86, 578891690, 578891716 87, 152374454, 152374465 88, 39500164, 39500169 89, 10176658, 10176660 90, 2632419, 2632420 91, 691000, 691001 92, 185987, 185987 93, 51814, 51814 94, 15036, 15036 95, 4583, 4583 96, 1471, 1471 97, 496, 496 98, 177, 177 99, 68, 68 100, 26, 26 101, 11, 11 102, 5, 5 103, 2, 2 104, 1, 1 105, 1, 1 totals: 31397381142761241960, 31426485969804308768 counts for n=16 0, 0, 1 1, 0, 1 2, 0, 2 3, 0, 5 4, 0, 11 5, 0, 26 6, 0, 68 7, 0, 177 8, 0, 497 9, 0, 1474 10, 0, 4601 11, 0, 15144 12, 0, 52496 13, 0, 190443 14, 0, 720298 15, 19320, 2821116 16, 311465, 11353457 17, 3042808, 46541024 18, 23118465, 192525021 19, 149685670, 796277250 20, 862572395, 3264731685 21, 4528544658, 13169762612 22, 21961480198, 51944608863 23, 99251914621, 199325942738 24, 420560727420, 741262597319 25, 1678281686360, 2663871179403 26, 6329077092453, 9231717579186 27, 22618117867415, 30807136431804 28, 76773365086100, 98902152234053 29, 247999842702735, 305278273828736 30, 763685360909770, 905723378795687 31, 2245154532231552, 2582678933141963 32, 6309879915290263, 7078696345634785 33, 16972802610729232, 18651996404491557 34, 43742890748220477, 47260851628555164 35, 108119250899529124, 115191335532066321 36, 256520586246582461, 270167167501687087 37, 584673421992357274, 609958885797372810 38, 1281134076961638346, 1326136343400463716 39, 2700579614533070386, 2777537605930232398 40, 5479829827952799857, 5606321256083832230 41, 10709494827604086670, 10909380006413889417 42, 20169093598306723982, 20472851567540820478 43, 36620483849338454029, 37064510246977549534 44, 64131220183281379663, 64755703757207605426 45, 108366231335871500301, 109211416604009007814 46, 176747716330872745639, 177848696079000172225 47, 278350098613104210378, 279730709445943481878 48, 423385461441565247736, 425052270572963469105 49, 622163407013949073453, 624101038803773627548 50, 883491393721262596160, 885660423533434300260 51, 1212617736381684350878, 1214956017367798514471 52, 1608989506687991413608, 1611417137591950662088 53, 2064259206012034697756, 2066686548593529103442 54, 2561070072143092759372, 2563407506160249980411 55, 3073125021226493922716, 3075292698315733707376 56, 3566867715628928049061, 3568803573245228168766 57, 4004789260291990621810, 4006453983295094401806 58, 4349984835162465146681, 4351363173523456284236 59, 4571224710742375695904, 4572323361987395717504 60, 4647586298937784001491, 4648429222263945620900 61, 4571700970421071914980, 4572323361987395717504 62, 4350920993620381139035, 4351363173523456284236 63, 4006151782717342115727, 4006453983295094401806 64, 3568604944103910221700, 3568803573245228168766 65, 3075167175805421897902, 3075292698315733707376 66, 2563331263109749220793, 2563407506160249980411 67, 2066642050873380637099, 2066686548593529103442 68, 1611392192597266839355, 1611417137591950662088 69, 1214942590399997790201, 1214956017367798514471 70, 885653486802431529240, 885660423533434300260 71, 624097600514858383973, 624101038803773627548 72, 425050636143463019881, 425052270572963469105 73, 279729964622586702774, 279730709445943481878 74, 177848370814214728354, 177848696079000172225 75, 109211280533389667566, 109211416604009007814 76, 64755649243571203894, 64755703757207605426 77, 37064489336439080294, 37064510246977549534 78, 20472843888563310367, 20472851567540820478 79, 10909377306471851409, 10909380006413889417 80, 5606320346884302466, 5606321256083832230 81, 2777537312500496686, 2777537605930232398 82, 1326136252540580428, 1326136343400463716 83, 609958858757339331, 609958885797372810 84, 270167159748279703, 270167167501687087 85, 115191333382542562, 115191335532066321 86, 47260851049663380, 47260851628555164 87, 18651996252117066, 18651996404491557 88, 7078696306134605, 7078696345634785 89, 2582678922965298, 2582678933141963 90, 905723376163265, 905723378795687 91, 305278273137734, 305278273828736 92, 98902152048065, 98902152234053 93, 30807136379990, 30807136431804 94, 9231717564150, 9231717579186 95, 2663871174820, 2663871179403 96, 741262595848, 741262597319 97, 199325942242, 199325942738 98, 51944608686, 51944608863 99, 13169762544, 13169762612 100, 3264731659, 3264731685 101, 796277239, 796277250 102, 192525016, 192525021 103, 46541022, 46541024 104, 11353456, 11353457 105, 2821115, 2821116 106, 720298, 720298 107, 190443, 190443 108, 52496, 52496 109, 15144, 15144 110, 4601, 4601 111, 1474, 1474 112, 497, 497 113, 177, 177 114, 68, 68 115, 26, 26 116, 11, 11 117, 5, 5 118, 2, 2 119, 1, 1 120, 1, 1 totals: 63969560113225176176277, 64001015704527557894928