A305650 a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).

1, 1, 9, 13, 61, 117, 421, 949, 2997, 7381, 21781, 56277, 160213, 424789, 1186389, 3189589, 8817493, 23883093, 65663317, 178568533, 489512277, 1334064469, 3651347797, 9962435925, 27244344661, 74380006741, 203315811669, 555257419093, 1517414896981, 4144807761237

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-2,-4).

Formula

a(n) = a(n-1) + 6*a(n-2) - 2*a(n-3) - 4*a(n-4) for n > 4.

G.f.: x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)). - Colin Barker, Jun 07 2018

Mathematica

LinearRecurrence[{1, 6, -2, -4}, {1, 1, 9, 13}, 30] (* Harvey P. Dale, Jun 02 2019 *)

Prog

(PARI) Vec(x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)) + O(x^40)) \\ Colin Barker, Jun 07 2018

Crossrefs

Cf. A129744.

Sequence in context: A365239 A271006 A271052 * A099580 A258286 A166662

Adjacent sequences: A305647 A305648 A305649 * A305651 A305652 A305653

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 07 2018

Status

approved