A123010 a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3), for n>4, with a(1)=1, a(2)=0, a(3)=4, a(4)=16.

1, 0, 4, 16, 84, 416, 2084, 10416, 52084, 260416, 1302084, 6510416, 32552084, 162760416, 813802084, 4069010416, 20345052084, 101725260416, 508626302084, 2543131510416, 12715657552084, 63578287760416, 317891438802084

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,1,-5).

Formula

O.g.f.: (1 -4*x -x^2)/((1+x)*(1-5*x)). - R. J. Mathar, Dec 05 2007

a(n) = (1/3)*(2*5^(n-2) - 2*(-1)^n) + (1/5)*0^(n-1). - Ridouane Oudra, Feb 22 2021

E.g.f.: (1/75)*(48 + 158x - 50*exp(-x) + 2*exp(5*x)). - G. C. Greubel, Jul 13 2021

Mathematica

LinearRecurrence[{5, 1, -5}, {1, 0, 4, 16}, 40] (* G. C. Greubel, Jul 13 2021 *)

Prog

(PARI) my(x='x+O('x^33)); Vec((x^2+4*x-1)/((x+1)*(5*x-1))) \\ Joerg Arndt, Feb 22 2021
(Sage) [1]+[(2/3)*(5^(n-2) - (-1)^n) for n in (2..40)] # G. C. Greubel, Jul 13 2021

Crossrefs

Sequence in context: A204066 A351816 A022564 * A121146 A134006 A366434

Adjacent sequences: A123007 A123008 A123009 * A123011 A123012 A123013

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 23 2006

Extensions

Edited by N. J. A. Sloane, Oct 15 2006

Edited by Joerg Arndt, Feb 22 2021

Status

approved