A297712 - OEIS

A297712

Number of irredundant sets in the n-dipyramidal graph.

7, 22, 29, 39, 60, 94, 151, 241, 400, 671, 1135, 1924, 3277, 5598, 9575, 16389, 28067, 48089, 82411, 141246, 242102, 414999, 711394, 1219497, 2090527, 3583720, 6143480, 10531637, 18054187, 30949982, 53057055, 90954885, 155922576, 267295733, 458221102, 785521661

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Irredundant Set

Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 2, -2, 0, 2, -1).

FORMULA

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-4) - 2*a(n-5) + 2*a(n-7) - a(n-8) for n > 11.

G.f.: x^3*(7 + x - 23*x^2 + 3*x^3 + 9*x^4 - 9*x^5 + 14*x^6 + 2*x^7 - 6*x^8)/((-1 + x)^2*(1 - x - x^2 - x^4 + x^6)).

MATHEMATICA

Table[Piecewise[{{7, n == 3}}, 3 + 2 n + RootSum[1 - #1^2 - #1^4 - #1^5 + #1^6 &, #^n &]], {n, 3, 20}]

Join[{7}, LinearRecurrence[{3, -2, -1, 2, -2, 0, 2, -1}, {22, 29, 39, 60, 94, 151, 241, 400}, 20]]

CoefficientList[Series[(7 + x - 23 x^2 + 3 x^3 + 9 x^4 - 9 x^5 + 14 x^6 + 2 x^7 - 6 x^8)/((-1 + x)^2 (1 - x - x^2 - x^4 + x^6)), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A070412 A286572 A055575 * A041090 A042639 A287166

Adjacent sequences: A297709 A297710 A297711 * A297713 A297714 A297715

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 18 2018

STATUS

approved