A350816 - OEIS

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A350816

Number of minimum dominating sets in the 2 X n king graph.

2, 4, 2, 16, 12, 4, 64, 32, 8, 208, 80, 16, 608, 192, 32, 1664, 448, 64, 4352, 1024, 128, 11008, 2304, 256, 27136, 5120, 512, 65536, 11264, 1024, 155648, 24576, 2048, 364544, 53248, 4096, 843776, 114688, 8192, 1933312, 245760, 16384, 4390912, 524288, 32768

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, King Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-12,0,0,8).

FORMULA

a(n) = 6*a(n-3) - 12*a(n-6) + 8*a(n-9) for n > 9.

G.f.: 2*x*(1 - x)*(1 + 3*x + 4*x^2 + 6*x^3 - 4*x^5 - 8*x^6 - 4*x^7)/(1 - 2*x^3)^3.

a(3*n) = 2^n; a(3*n+1) = (n^2 + 5*n + 2)*2^n; a(3*n+2) = (n + 2)*2^(n+1).