A291063 Number of maximal irredundant sets in the n-wheel graph.

1, 3, 4, 7, 11, 12, 15, 15, 31, 63, 67, 100, 144, 213, 344, 479, 698, 993, 1502, 2247, 3252, 4777, 6970, 10284, 15211, 22298, 32728, 47985, 70645, 103962, 152707, 224383, 329509, 484452, 712275, 1046737, 1538165, 2260110, 3321933, 4882575, 7175739

Offset

2,2

Comments

The wheel graph is well defined for n >= 4. Sequence extended to n=2 using formula. - Andrew Howroyd, Aug 19 2017

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Eric Weisstein's World of Mathematics, Maximal Irredundant Set

Eric Weisstein's World of Mathematics, Wheel Graph

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

Formula

a(n) = A286954(n-1) + 1. - Andrew Howroyd, Aug 19 2017

G.f.: x^2*(1 + 2*x - 6*x^5 - 7*x^6 - 8*x^7 + 9*x^8 + 30*x^9 - 11*x^10 - 12*x^11 - 14*x^13 + 15*x^14) / ((1 - x)*(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14)). - Colin Barker, Aug 20 2017

Mathematica

Table[1 + RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, #^(n - 1) &], {n, 2, 20}]
1 + RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, #^Range[20] &]
LinearRecurrence[{1, 1, 0, 0, 0, -1, -1, -1, 1, 3, -1, -1, 0, -1, 1}, {1, 3, 4, 7, 11, 12, 15, 15, 31, 63, 67, 100, 144, 213, 344}, 20]
CoefficientList[
Series[(1 + 2 x - 6 x^5 - 7 x^6 - 8 x^7 + 9 x^8 + 30 x^9 - 11 x^10 - 12 x^11 - 14 x^13 + 15 x^14)/((1 - x) (1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2 x^8 + x^9 - 2 x^10 - x^11 + x^14)), {x, 0, 20}], x]

Prog

(PARI) Vec(x^2*(1 + 2*x - 6*x^5 - 7*x^6 - 8*x^7 + 9*x^8 + 30*x^9 - 11*x^10 - 12*x^11 - 14*x^13 + 15*x^14) / ((1 - x)*(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14)) + O(x^60)) \\ Colin Barker, Aug 20 2017

Crossrefs

Cf. A286954, A290494.

Sequence in context: A185506 A328379 A080591 * A047543 A030489 A132841

Adjacent sequences: A291060 A291061 A291062 * A291064 A291065 A291066

Keyword

nonn

Author

Eric W. Weisstein, Aug 17 2017

Extensions

a(2)-a(3) and a(21)-a(42) from Andrew Howroyd, Aug 19 2017

Status

approved