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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.
9
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
2,2
COMMENTS
The number of vertices is n - k.
Column k is a polynomial of degree 3*k. This is because adding a face can increase the number of vertices whose degree is greater than two by at most two.
LINKS
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.
EXAMPLE
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;
...
PROG
(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])) }
CROSSREFS
Columns 1..2 are A000292, A006469.
Diagonals are A002802, A006425, A006426, A006427.
Row sums are A343093.
Sequence in context: A264163 A223165 A263558 * A346751 A292910 A292954
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 04 2021
STATUS
approved