A287062 Number of dominating sets in the 2n-crossed prism graph.

11, 183, 2417, 32499, 436281, 5857683, 78646537, 1055926979, 14177123321, 190345385523, 2555621823337, 34312378451619, 460686046833881, 6185278996234003, 83045007601555017, 1114981764240774019, 14970006873311301561, 200990826015513435123

Offset: 1

Author

Eric W. Weisstein, May 19 2017

Keywords

• nonn

Comments

Sequence extended to n=1 using recurrence. - Andrew Howroyd, May 21 2017

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Crossed Prism Graph
• Eric Weisstein's World of Mathematics, Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (11, 31, 21, 2).

Programs

Mathematica

LinearRecurrence[{11, 31, 21, 2}, {11, 183, 2417, 32499}, 20] (* Eric W. Weisstein, May 27 2017 *)
Table[(-1)^n + RootSum[-2 - 19 # - 12 #^2 + #^3 &, #^n &], {n, 20}] (* Eric W. Weisstein, May 27 2017 *)

PARI

Vec((11+62*x+63*x^2+8*x^3)/((1+x)*(1-12*x-19*x^2-2*x^3)) + O(x^20)) \\ Andrew Howroyd, May 21 2017

Formula

From Andrew Howroyd, May 21 2017 (Start)

a(n) = 11*a(n-1)+31*a(n-2)+21*a(n-3)+2*a(n-4).

G.f.: x*(11+62*x+63*x^2+8*x^3)/((1+x)*(1-12*x-19*x^2-2*x^3)).

(End)

Extensions

a(1) and a(8)-a(18) from Andrew Howroyd, May 21 2017