A286986 Number of connected dominating sets in the n-antiprism graph.

3, 15, 54, 175, 543, 1642, 4875, 14271, 41310, 118487, 337263, 953810, 2682579, 7508655, 20929158, 58121407, 160877055, 443993146, 1222110555, 3355879647, 9195143598, 25144855655, 68635721679, 187035899810, 508896450723, 1382653280847, 3751638404310

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Connected Dominating Set

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Formula

From G. C. Greubel, May 17 2017: (Start)

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

G.f.: (3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4). (End)

Mathematica

Table[6 n ChebyshevU[n - 1, 3/2] + (1 - 2 n) LucasL[2 n], {n, 30}] (* Eric W. Weisstein, May 17 2017 *)
LinearRecurrence[{6, -11, 6, -1}, {3, 15, 54, 175}, 30] (* Eric W. Weisstein, May 17 2017 *)
Rest[CoefficientList[Series[(3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4), {x, 0, 50}], x]] (* G. C. Greubel, May 17 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((3*x - 3*x^2 - 3*x^3 - 2*x^4)/(1 - 6*x + 11*x^2 - 6*x^3 + x^4)) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A298178 A147618 A290764 * A261565 A085480 A265974

Adjacent sequences: A286983 A286984 A286985 * A286987 A286988 A286989

Keyword

nonn

Author

Eric W. Weisstein, May 17 2017

Status

approved