A291772 Number of minimal dominating sets in the 2n-crossed prism graph.

4, 12, 61, 316, 1304, 5223, 21557, 90404, 377863, 1572942, 6545785, 27262279, 113572619, 473082153, 1970443556, 8207168564, 34184621296, 142386794787, 593071821262, 2470268797246, 10289192009129, 42856677944829, 178507203892808, 743520516941183

Offset: 1

Author

Eric W. Weisstein, Aug 31 2017

Keywords

• nonn

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, Minimal Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (4,-2,7,17,2).

Crossrefs

Cf. A287062, A290708.

Programs

Mathematica

Rest@ CoefficientList[Series[x (4 - 4 x + 21 x^2 + 68 x^3 + 10 x^4)/(1 - 4 x + 2 x^2 - 7 x^3 - 17 x^4 - 2 x^5), {x, 0, 24}], x] (* Michael De Vlieger, Aug 31 2017 *)
LinearRecurrence[{4,-2,7,17,2},{4,12,61,316,1304},30] (* Harvey P. Dale, Jul 02 2019 *)
Table[RootSum[-2 - 17 # - 7 #^2 + 2 #^3 - 4 #^4 + #^5 &, #^n &], {n, 20}] (* Eric W. Weisstein, Sep 08 2021 *)

PARI

Vec((4 - 4*x + 21*x^2 + 68*x^3 + 10*x^4)/(1 - 4*x + 2*x^2 - 7*x^3 - 17*x^4 - 2*x^5)+O(x^30)) \\ Andrew Howroyd, Aug 31 2017

PARI

\\ sequence prepended by a 5:
polsym(-2 - 17*x - 7*x^2 + 2*x^3 - 4*x^4 + x^5, 24) \\ Joerg Arndt, Sep 08 2021

Formula

From Andrew Howroyd, Aug 31 2017: (Start)

a(n) = 4*a(n-1) - 2*a(n-2) + 7*a(n-3) + 17*a(n-4) + 2*a(n-5) for n > 5.

G.f.: x*(4 - 4*x + 21*x^2 + 68*x^3 + 10*x^4)/(1 - 4*x + 2*x^2 - 7*x^3 - 17*x^4 - 2*x^5).

(End)

Extensions

a(1) and terms a(7) and beyond from Andrew Howroyd, Aug 31 2017