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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

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OFFSET

0,2

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).

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.

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 *)

PROG

(Haskell)

a048877 n = a048877_list !! n

a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)

-- Reinhard Zumkeller, May 01 2013

CROSSREFS

Cf. A015448, A001076, A001077, A033887.

Sequence in context: A317017 A283544 A212404 * A349101 A297683 A346819

Adjacent sequences: A048874 A048875 A048876 * A048878 A048879 A048880

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams

STATUS

approved

URL: https://oeis.org/A048877

⇱ A048877 - OEIS