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.
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
Examples
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; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..1276
- T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259, Table VId.
Crossrefs
Programs
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PARI
\\ 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])) }
Comments