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A343092
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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.
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9
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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
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OFFSET
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2,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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;
...
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PROG
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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])) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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