|
|
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.
|
|
8
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
T(n,n-k) = T(n,k).
|
|
EXAMPLE
|
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;
...
|
|
PROG
|
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])) }
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|