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

Author

Eric W. Weisstein, Aug 17 2017

Keywords

• nonn

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).

Crossrefs

Cf. A286954, A290494.

Programs

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]

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

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

Extensions

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