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A290588
Number of irredundant sets in the n-helm graph.
0
5, 13, 35, 113, 355, 1105, 3435, 10625, 32723, 100433, 307323, 937985, 2856547, 8682897, 26349835, 79850241, 241679859, 730700881, 2207155867, 6661493633, 20090908803, 60555714705, 182419600683, 549259559297, 1653098625555, 4973441442385, 14957936920763
OFFSET
1,1
COMMENTS
Extended to a(1)-a(2) using the recurrence.
LINKS
Eric Weisstein's World of Mathematics, Helm Graph
Eric Weisstein's World of Mathematics, Irredundant Set
FORMULA
a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5).
G.f.: (x (-5 + 17 x - 7 x^2 - 13 x^3))/(-1 + 6 x - 10 x^2 + 4 x^3 - 5 x^4 + 6 x^5).
MATHEMATICA
Table[1 + 2 3^n - RootSum[-2 - # - 2 #^2 + #^3 &, #^n &], {n, 20}]
LinearRecurrence[{6, -10, 4, -5, 6}, {5, 13, 35, 113, 355}, 20]
CoefficientList[Series[(-5 + 17 x - 7 x^2 - 13 x^3)/(-1 + 6 x - 10 x^2 + 4 x^3 - 5 x^4 + 6 x^5), {x, 0, 20}], x]
CROSSREFS
Sequence in context: A167710 A229924 A264080 * A272149 A272560 A266102
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 07 2017
EXTENSIONS
a(12)-a(16) from Andrew Howroyd, Aug 11 2017
STATUS
approved