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A122690 a(0)=1, a(1)=4, a(n)=5*a(n-1)+4*a(n-2) for n>1. 6
1, 4, 24, 136, 776, 4424, 25224, 143816, 819976, 4675144, 26655624, 151978696, 866515976, 4940494664, 28168537224, 160604664776, 915697472776, 5220906022984, 29767320006024, 169720224122056, 967670400634376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,4).

FORMULA

a(n)=Sum_{k, 0<=k<=n} 4^k*A122542(n,k) . G.f. (1-x)/(1-5*x-4*x^2). a(n+1)/a(n)-> (5+sqrt(41))/2 = 5.701562118716...if n-> infinity.

a(n)=(1/2)*[5/2-(1/2)*sqrt(41)]^n+(3/82)*sqrt(41)*[5/2+(1/2)*sqrt(41)]^n-(3/82)*sqrt(41)*[5/2-(1 /2)*sqrt(41)]^n+(1/2)*[5/2+(1/2)*sqrt(41)]^n, with n>=0 - Paolo P. Lava, Jul 07 2008

MATHEMATICA

LinearRecurrence[{5, 4}, {1, 4}, 30] (* Harvey P. Dale, Apr 06 2012 *)

PROG

(PARI) Vec((1-x)/(1-5*x-4*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 17 2012

CROSSREFS

Sequence in context: A057391 A071079 A153337 * A183512 A204199 A262376

Adjacent sequences:  A122687 A122688 A122689 * A122691 A122692 A122693

KEYWORD

nonn,easy,less

AUTHOR

Philippe Deléham, Sep 22 2006

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

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Last modified September 17 19:02 EDT 2019. Contains 327137 sequences. (Running on oeis4.)