A048877 a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8.

1, 8, 33, 140, 593, 2512, 10641, 45076, 190945, 808856, 3426369, 14514332, 61483697, 260449120, 1103280177, 4673569828, 19797559489, 83863807784, 355252790625, 1504874970284, 6374752671761

Offset: 0

Author

Barry E. Williams

Keywords

• easy
• nonn

Comments

Generalized Pellian with second term of 8.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (4,1).

Crossrefs

Cf. A015448, A001076, A001077, A033887.

Programs

Haskell

a048877 n = a048877_list !! n
a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)
-- Reinhard Zumkeller, May 01 2013

Maple

with(combinat): a:=n->4*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008

Mathematica

CoefficientList[Series[(1+4x)/(1-4x-x^2),{x,0,20}],x]  (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{4,1},{1,8},30] (* Harvey P. Dale, Nov 03 2013 *)

Formula

a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).

G.f.: (1+4*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008

a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.