A382777 Number of minimum total dominating sets in the (3n)-triangular honeycomb bishop graph.

1, 2, 21, 540, 25740, 1965600, 219769200, 33844456800, 6868433880000, 1776393899280000, 570349326947400000, 222585024290428800000, 103769138324197906560000, 56957727035726406489600000, 36357688414546530128697600000, 26705308554813693259046592000000, 22364482036994885663848836864000000

Offset

0,2

Comments

The total domination number is 2*n.

Links

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.

Eric Weisstein's World of Mathematics, Triangular Honeycomb Bishop Graph.

Formula

a(n) = Sum_{k=0..n} binomial(2*n-k,k)*binomial(n+k,n-k)*(2*(n-k))!*(2*k)!/(2^n).

a(n) = A304564(3*n) for n > 0.

a(n) ~ sqrt(Pi) * 3^(3*n + 3/2) * n^(2*n + 1/2) / (2^(3*n+1) * exp(2*n)). - Vaclav Kotesovec, Feb 07 2026

Mathematica

Table[Sum[Binomial[2*n-k, k]*Binomial[n+k, n-k]*(2*(n-k))!*(2*k)!/(2^n), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 07 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(2*n-k, k)*binomial(n+k, n-k)*(2*(n-k))!*(2*k)!)/(2^n)

Crossrefs

Row sums of A382776.

Cf. A304564.

Sequence in context: A158886 A092957 A356481 * A171107 A218768 A195736

Adjacent sequences: A382774 A382775 A382776 * A382778 A382779 A382780

Keyword

nonn

Author

Andrew Howroyd, Apr 04 2025

Status

approved