A343092
Triangle read by rows: T(n,k) is the number of rooted toroidal maps with n edges and k faces and without isthmuses, n >= 2, k = 1..n-1.
Original entry on oeis.org
1, 4, 10, 10, 79, 70, 20, 340, 900, 420, 35, 1071, 5846, 7885, 2310, 56, 2772, 26320, 71372, 59080, 12012, 84, 6258, 93436, 431739, 706068, 398846, 60060, 120, 12768, 280120, 2000280, 5494896, 6052840, 2499096, 291720, 165, 24090, 739420, 7643265, 32055391, 58677420, 46759630, 14805705, 1385670
Offset: 2
Triangle begins:
1;
4, 10;
10, 79, 70;
20, 340, 900, 420;
35, 1071, 5846, 7885, 2310;
56, 2772, 26320, 71372, 59080, 12012;
84, 6258, 93436, 431739, 706068, 398846, 60060;
...
-
\\ Needs F from A342989.
G(n,m,y,z)={my(p=F(n,m,y,z)); subst(p, x, serreverse(x*p^2))}
H(n, g=1)={my(q=G(n, g, 'y, 'z)-x, v=Vec(polcoef(sqrt(serreverse(x/q^2)/x), g, 'y))); [Vecrev(t) | t<-v]}
{ my(T=H(10)); for(n=1, #T, print(T[n])) }
A343090
Triangle read by rows: T(n,k) is the number of rooted toroidal maps with n edges and k faces and without separating cycles or isthmuses, n >= 2, k = 1..n-1.
Original entry on oeis.org
1, 4, 4, 10, 47, 10, 20, 240, 240, 20, 35, 831, 2246, 831, 35, 56, 2282, 12656, 12656, 2282, 56, 84, 5362, 52164, 109075, 52164, 5362, 84, 120, 11256, 173776, 648792, 648792, 173776, 11256, 120, 165, 21690, 495820, 2978245, 5360286, 2978245, 495820, 21690, 165
Offset: 2
Triangle begins:
1;
4, 4;
10, 47, 10;
20, 240, 240, 20;
35, 831, 2246, 831, 35;
56, 2282, 12656, 12656, 2282, 56;
84, 5362, 52164, 109075, 52164, 5362, 84;
120, 11256, 173776, 648792, 648792, 173776, 11256, 120;
...
-
\\ Needs F from A342989.
G(n,m,y,z)={my(p=F(n,m,y,z)); subst(p, x, serreverse(x*p^2))}
H(n, g=1)={my(q=G(n, g, 'y, 'z)-x*(1+'z), v=Vec(polcoef(sqrt(serreverse(x/q^2)/x), g, 'y))); [Vecrev(t) | t<-v]}
{ my(T=H(10)); for(n=1, #T, print(T[n])) }
A006408
Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.
Original entry on oeis.org
4, 39, 190, 651, 1792, 4242, 8988, 17490, 31812, 54769, 90090, 142597, 218400, 325108, 472056, 670548, 934116, 1278795, 1723414, 2289903, 3003616, 3893670, 4993300, 6340230, 7977060, 9951669, 12317634, 15134665, 18469056, 22394152, 26990832, 32348008, 38563140
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006409
Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices.
Original entry on oeis.org
10, 190, 1568, 8344, 33580, 111100, 317680, 811096, 1891318, 4094090, 8328320, 16071120, 29636984, 52540472, 89974880, 149432720, 241497410, 380839382, 587453856, 888181800, 1318560100, 1925051700, 2767711440, 3923348520, 5489251950, 7587551010, 10370288640
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A006410
Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices.
Original entry on oeis.org
20, 651, 8344, 64667, 361884, 1607125, 5997992, 19535997, 57014776, 151986562, 375470160, 869285378, 1902886024, 3966657702, 7920130544, 15220758070, 28268206764, 50910912965, 89176474920, 152305796565, 254193384900, 415363487955, 665644575960, 1047743815755
Offset: 2
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A343089
Number of nonseparable rooted toroidal maps with n edges.
Original entry on oeis.org
1, 8, 59, 420, 2940, 20384, 140479, 964184, 6598481, 45059872, 307197620, 2091615760, 14226362200, 96680047568, 656559634503, 4456100344560, 30228597199443, 204971912361512, 1389342336011059, 9414200925647540, 63772600432265968, 431892497914345472
Offset: 2
Showing 1-6 of 6 results.
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