A284699 Number of dominating sets in the n-antiprism graph.

3, 15, 57, 223, 863, 3333, 12883, 49791, 192441, 743775, 2874655, 11110405, 42941187, 165965647, 641449337, 2479171199, 9581878847, 37033506309, 143132741651, 553201243263, 2138096511097, 8263641389887, 31938581194175, 123441098248197, 477093977471363, 1843945546253839, 7126761892007865

Offset

1,1

Comments

Recurrence used to extrapolate sequence to a(1) and a(2).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Dominating Set

Index entries for linear recurrences with constant coefficients, signature (3,3,1,1,1).

Formula

From Colin Barker, Apr 01 2017: (Start)

G.f.: x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5).

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

(End)

Mathematica

LinearRecurrence[{3, 3, 1, 1, 1}, {3, 15, 57, 223, 863, 3333, 12883}, 20]
Table[RootSum[-1 - # - #^2 - 3 #^3 - 3 #^4 + #^5 &, #^n &], {n, 20}]

Prog

(PARI) Vec(x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5) + O(x^30)) \\ Colin Barker, Apr 01 2017

Crossrefs

Sequence in context: A358685 A118048 A210448 * A218657 A218804 A125673

Adjacent sequences: A284696 A284697 A284698 * A284700 A284701 A284702

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 01 2017

Status

approved