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

Author

Andrew Howroyd, Apr 04 2025

Keywords

• nonn

Comments

The total domination number is 2*n.

Links

• Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
• Eric Weisstein's World of Mathematics, Triangular Honeycomb Bishop Graph.

Crossrefs

Row sums of A382776.

Cf. A304564.

Programs

PARI

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

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.