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

1,1

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).

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).

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 *)

Prog

(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))

Crossrefs

Row 2 of A286849.

Sequence in context: A248334 A001774 A053285 * A228119 A078148 A076075

Adjacent sequences: A286847 A286848 A286849 * A286851 A286852 A286853

Keyword

nonn

Author

Andrew Howroyd, Aug 01 2017

Status

approved