A347536 Number of minimum dominating sets in the complete tripartite graph K_n,n,n.

3, 15, 27, 48, 75, 108, 147, 192, 243, 300, 363, 432, 507, 588, 675, 768, 867, 972, 1083, 1200, 1323, 1452, 1587, 1728, 1875, 2028, 2187, 2352, 2523, 2700, 2883, 3072, 3267, 3468, 3675, 3888, 4107, 4332, 4563, 4800, 5043, 5292, 5547, 5808, 6075, 6348, 6627

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Eric Weisstein's World of Mathematics, Complete Tripartite Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = A033428(n) = 3*n^2 for n != 2.

G.f.: 3*x*(-1 - 2*x + 3*x^2 - 3*x^3 + x^4)/(-1 + x)^3.

From Stefano Spezia, Sep 06 2021: (Start)

E.g.f.: 3*x*(x + 2*exp(x)*(1 + x))/2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5. (End)

Crossrefs

Cf. A291537, A290325.

Sequence in context: A080065 A017557 A147041 * A002259 A050848 A077785

Adjacent sequences: A347533 A347534 A347535 * A347537 A347538 A347539

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 05 2021

Status

approved