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A297712 Number of irredundant sets in the n-dipyramidal graph. 1
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

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)