A290588 Number of irredundant sets in the n-helm graph.

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

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Helm Graph

Eric Weisstein's World of Mathematics, Irredundant Set

Index entries for linear recurrences with constant coefficients, signature (6, -10, 4, -5, 6).

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

Adjacent sequences: A290585 A290586 A290587 * A290589 A290590 A290591

Keyword

nonn

Author

Eric W. Weisstein, Aug 07 2017

Extensions

a(12)-a(16) from Andrew Howroyd, Aug 11 2017

Status

approved