A303144 Number of minimum total dominating sets in the n X n white bishop graph.

1, 4, 1, 4, 61, 12, 104, 2540, 270, 5760, 184710, 13140, 458640, 20036160, 982800, 53726400, 3042295200, 110224800, 8497742400, 611011447200, 16922228400, 1763683891200, 157184659447200, 3435788664000, 463679536320000, 50243200517664000, 888196949640000, 150876035934624000, 19562163412303512000

Offset: 2

Author

Eric W. Weisstein, Apr 19 2018

Keywords

• nonn

Comments

For n >= 3, the total domination number is given by floor(2*n/3) = A004523(n). - Andrew Howroyd, May 17 2025

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..200
• Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
• Eric Weisstein's World of Mathematics, White Bishop Graph.

Crossrefs

Cf. A303141 (black bishop).

Cf. A004523, A303147, A303229, A321673.

Programs

PARI

vector(29,n,A303144(n+1)) \\ See PARI link in A321673 for program code. - Andrew Howroyd, May 17 2025

Extensions

a(8)-a(10) from Andrew Howroyd, Apr 20 2018

a(11) from Eric W. Weisstein, Apr 02 2025

a(12) onwards from Andrew Howroyd, May 16 2025