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

Author

Eric W. Weisstein, May 17 2017

Keywords

• nonn
• easy

Links

• 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).

Programs

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 *)

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

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

a(n) = 28*A001871(n) -72*A001871(n-1) -15*A001906(n)-26*A001906(n+1). - R. J. Mathar, Dec 16 2024