A290938 Number of dominating sets in the n-gear graph.

5, 23, 83, 291, 1015, 3539, 12339, 43043, 150239, 524723, 1833771, 6412467, 22437095, 78553491, 275180323, 964534339, 3382685743, 11869824179, 41673547291, 146387820371, 514484547639, 1809077492883, 6364347723667, 22400458807139, 78878848178815, 277881197881011

Offset

1,1

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Table of n, a(n) for n=1..26.

James East, Jitender Kumar, James D.Mitchell, Wilf A. Wilson, Maximal subsemigroups of finite transformation and diagram monoids, Journal of Algebra (2018), 504, 176-216, arXiv:1706.04967 [math.GR], 2017-2018.

Eric Weisstein's World of Mathematics, Dominating Set

Eric Weisstein's World of Mathematics, Gear Graph

Index entries for linear recurrences with constant coefficients, signature (7, -12, -2, 3, 3, 2).

Formula

a(n) = 7*a(n-1) - 12*a(n-2) - 2*a(n-3) + 3*a(n-4) + 3*a(n-5) + 2*a(n-6).

G.f.: (x (-5 + 12 x + 18 x^2 + 4 x^3 - 5 x^4 - 8 x^5))/(-1 + 7 x - 12 x^2 - 2 x^3 + 3 x^4 + 3 x^5 + 2 x^6).

Mathematica

Table[(1/2 (3 - Sqrt[17]))^n + (1/2 (3 + Sqrt[17]))^n - 1 + RootSum[-1 - # - 3 #^2 + #^3 &, #^n &], {n, 20}] // Expand
LinearRecurrence[{7, -12, -2, 3, 3, 2}, {5, 23, 83, 291, 1015, 3539}, 20]
CoefficientList[Series[(-5 + 12 x + 18 x^2 + 4 x^3 - 5 x^4 - 8 x^5)/(-1 + 7 x - 12 x^2 - 2 x^3 + 3 x^4 + 3 x^5 + 2 x^6), {x, 0, 20}], x]

Crossrefs

Cf. A290378 (minimal dominating sets).

Sequence in context: A227123 A113946 A283114 * A193696 A377496 A147359

Adjacent sequences: A290935 A290936 A290937 * A290939 A290940 A290941

Keyword

nonn

Author

Eric W. Weisstein, Aug 14 2017

Status

approved