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.
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
Examples
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;
...
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 VIc.
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*(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])) }
Formula
T(n,n-k) = T(n,k).
Comments