A286850 Number of minimal dominating sets in the 2 X n king graph.

2, 4, 6, 16, 20, 52, 80, 176, 296, 592, 1104, 2064, 3936, 7296, 14048, 25984, 49600, 92736, 175872, 330240, 623232, 1175296, 2213632, 4176128, 7863808, 14838784, 27948544, 52707328, 99320832, 187257856, 352940032, 665276416, 1254090752, 2363805696, 4455927808

Offset: 1

Author

Andrew Howroyd, Aug 01 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, King Graph
• Eric Weisstein's World of Mathematics, Minimal Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (0, 2, 2, 4, 0, -8).

Crossrefs

Row 2 of A286849.

Programs

Mathematica

Table[RootSum[8 - 4 #1^2 - 2 #1^3 - 2 #1^4 + #1^6 &, 36 #1^n - 36 #1^(2 + n) + 55 #1^(3 + n) - 3 #1^(4 + n) + 32 #1^(5 + n) &]/970, {n, 10}] (* Eric W. Weisstein, Aug 04 2017 *)
LinearRecurrence[{0, 2, 2, 4, 0, -8}, {2, 4, 6, 16, 20, 52}, 20] (* Eric W. Weisstein, Aug 03 2017 *)
CoefficientList[Series[-((2 (-1 - 2 x - x^2 - 2 x^3 + 4 x^4 + 4 x^5))/(1 - 2 x^2 - 2 x^3 - 4 x^4 + 8 x^6)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 03 2017 *)

PARI

Vec(2*(1+2*x+x^2+2*x^3-4*x^4-4*x^5)/(1-2*x^2-2*x^3-4*x^4+8*x^6)+O(x^40))

Formula

a(n) = 2*a(n-2)+2*a(n-3)+4*a(n-4)-8*a(n-6) for n>6.

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