A290494 Number of irredundant sets in the n-wheel graph.

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

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