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

Author

Eric W. Weisstein, Aug 04 2017

Keywords

• nonn

Links

• 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).

Programs

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]

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) ).