A144479 a(0)=1, a(1)=3, a(n) = 8*a(n-1) - a(n-2).

1, 3, 23, 181, 1425, 11219, 88327, 695397, 5474849, 43103395, 339352311, 2671715093, 21034368433, 165603232371, 1303791490535, 10264728691909, 80814038044737, 636247575665987, 5009166567283159, 39437084962599285, 310487513133511121, 2444463020105489683

Offset: 0

Author

N. J. A. Sloane, Mar 28 2009

Keywords

• nonn
• easy

Comments

A105426 extended backwards.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (8, -1).

Programs

Magma

I:=[1,3]; [n le 2 select I[n] else 8*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 12 2015

Mathematica

LinearRecurrence[{8, -1}, {1, 3}, 25] (* Vincenzo Librandi, Oct 12 2015 *)

PARI

Vec((1-5*x)/(1-8*x+x^2) + O(x^40)) \\ Colin Barker, Oct 12 2015

Formula

G.f.: (1-5*x)/(1-8*x+x^2). - Philippe Deléham, Mar 28 2009

a(n) = A001090(n+1)-5*A001090(n). - R. J. Mathar, Mar 29 2009

a(n) = (((4-sqrt(15))^n*(1+sqrt(15))+(-1+sqrt(15))*(4+sqrt(15))^n))/(2*sqrt(15)). - Colin Barker, Oct 12 2015

Extensions

More terms from Philippe Deléham and R. J. Mathar, Mar 28 2009