A212800 Number of spanning trees of the (n,n)-torus grid graph.

1, 32, 11664, 42467328, 1562500000000, 587312954081280000, 2266101334892340404752384, 89927963805390785392395474173952, 36735015407753190053984060991247792275456, 154528563849617762057150663767149772800000000000000, 6695315138840257072470706538467584763944601124280722177130496

Offset: 1

Author

N. J. A. Sloane, May 27 2012

Keywords

• nonn

Comments

Main diagonal of array in A212796.

Links

• Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Para. 4.
• Eric Weisstein's World of Mathematics, Spanning Tree
• Eric Weisstein's World of Mathematics, Torus Grid Graph

Crossrefs

Cf. A212796, A340562.

Programs

Mathematica

Table[n^2 * Product[4*Sin[j*Pi/n]^2 + 4*Sin[k*Pi/n]^2, {k, 1, n-1}, {j, 1, n-1}], {n, 1, 12}] // Round (* Vaclav Kotesovec, Feb 14 2021 *)

Formula

a(n) ~ Gamma(1/4)^4 * exp(4*G*n^2/Pi) / (16 * Pi^3), where G is Catalan's constant A006752. - Vaclav Kotesovec, Feb 14 2021

Extensions

More terms from Eric W. Weisstein, May 10 2017