A303211 Number of minimum total dominating sets in the n X n rook graph.

0, 4, 6, 80, 410, 5112, 48818, 695424, 9589266, 162327800, 2869193162, 57451559904, 1225220612954, 28560612445848, 709917843398850, 18943086191785472, 536695850359985186, 16151064034012994808, 513345798896635886906, 17206881800061632191200

Offset: 1

Author

Eric W. Weisstein, Apr 19 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
• Eric Weisstein's World of Mathematics, Rook Graph.

Crossrefs

Main diagonal of A384117.

Cf. A248744, A303208, A347921.

Programs

Mathematica

Table[(-1)^n n! + Sum[(-1)^k Binomial[n, k]^2 k! (2 (n - k)^(n - k) - (n - k)!), {k, 0, n - 1}], {n, 20}]
2 Table[(-1)^n n! + Sum[(-1)^k Binomial[n, k]^2 k! (n - k)^(n - k), {k, 0, n - 1}], {n, 20}] (* Eric W. Weisstein, Jan 18 2019 *)

PARI

a(n) = {sum(k=0, n, (-1)^k*binomial(n,k)^2*k!*(2*(n-k)^(n-k) - (n-k)!))} \\ Andrew Howroyd, Apr 20 2018

Formula

a(n) = Sum_{k=0,..n} (-1)^k*binomial(n,k)^2*k!*(2*(n-k)^(n-k) - (n-k)!). - Andrew Howroyd, Apr 20 2018

a(n) ~ 2 * (exp(1) - 1)^(n + 1/2) * n^n / exp(n + 1/2). - Vaclav Kotesovec, Apr 20 2018

Extensions

Terms a(6) and beyond from Andrew Howroyd, Apr 20 2018