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A290494 Number of irredundant sets in the n-wheel graph. 1
5, 12, 17, 25, 44, 76, 131, 219, 376, 645, 1107, 1894, 3245, 5564, 9539, 16351, 28027, 48047, 82367, 141200, 242054, 414949, 711342, 1219443, 2090471, 3583662, 6143420, 10531575, 18054123, 30949916, 53056987, 90954815, 155922504, 267295659, 458221026 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Table of n, a(n) for n=4..38.

Eric Weisstein's World of Mathematics, Irredundant Set

Eric Weisstein's World of Mathematics, Wheel Graph

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

FORMULA

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

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

MATHEMATICA

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

LinearRecurrence[{2, 0, -1, 1, -1, -1, 1}, {5, 12, 17, 25, 44, 76, 131}, 20]

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

CROSSREFS

Sequence in context: A314287 A135459 A214067 * A246787 A246810 A063297

Adjacent sequences:  A290491 A290492 A290493 * A290495 A290496 A290497

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Aug 04 2017

STATUS

approved

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Last modified May 13 23:41 EDT 2021. Contains 343868 sequences. (Running on oeis4.)