OFFSET
1,2
LINKS
Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Parag. 4.
Eric Weisstein's World of Mathematics, Spanning Tree
Eric Weisstein's World of Mathematics, Torus Grid Graph
FORMULA
T(m,n) = m*n*Prod(Prod( 4*sin(h*Pi/m)^2+4*sin(k*Pi/n)^2, h=1..m-1), k=1..n-1).
EXAMPLE
Array begins:
1, 2, 3, 4, 5, 6 7, ...
2, 32, 294, 2304, 16810, 117600, 799694, ...
3, 294, 11664, 367500, 10609215, 292626432, 7839321861, ...
4, 2304, 367500, 42467328, 4381392020, 428652000000, 40643137651228, ...
...
MAPLE
Digits:=200;
T:=(m, n)->round(Re(evalf(simplify(expand(
m*n*mul(mul( 4*sin(h*Pi/m)^2+4*sin(k*Pi/n)^2, h=1..m-1), k=1..n-1))))));
PROG
(PARI) default(realprecision, 120);
{T(n, k) = round(n*k*prod(a=1, n-1, prod(b=1, k-1, 4*sin(a*Pi/n)^2+4*sin(b*Pi/k)^2)))} \\ Seiichi Manyama, Jan 13 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 27 2012
STATUS
approved