A347481 Number of total dominating sets in the n-dipyramidal graph.

4, 10, 25, 54, 104, 205, 410, 814, 1609, 3190, 6340, 12609, 25094, 49990, 99665, 198814, 396784, 792205, 1582210, 3160854, 6315929, 12622510, 25229900, 50435329, 100831054, 201598030, 403092385, 806017014, 1611762584, 3223085965, 6445461290, 12889772734

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (4,-5,3,-2,-1,2).

Formula

a(n) = Lucas(n) + 2*cos(n*Pi/2) + 3*2^n - 3.

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

G.f.: -(x*(4 - 6*x + 5*x^2 - 8*x^3 - 9*x^4 + 8*x^5)/((-1 + x)*(-1 +

2*x)*(1 + x^2)*(-1 + x + x^2)).

Mathematica

Table[LucasL[n] + 2 Cos[n Pi/2] + 3 2^n - 3, {n, 50}]
LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 10, 25, 54, 104, 205}, 20]
CoefficientList[Series[-(4 - 6 x + 5 x^2 - 8 x^3 - 9 x^4 + 8 x^5)/((-1 + x) (-1 + 2 x) (1 + x^2) (-1 + x + x^2)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A298018 A254233 A300760 * A229916 A113412 A227712

Adjacent sequences: A347478 A347479 A347480 * A347482 A347483 A347484

Keyword

nonn

Author

Eric W. Weisstein, Sep 03 2021

Status

approved