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
Keywords
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).
Programs
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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
Comments