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A123270 a(0)=1, a(1)=1, a(n)=5*a(n-1)+4*a(n-2). 6
1, 1, 9, 49, 281, 1601, 9129, 52049, 296761, 1692001, 9647049, 55003249, 313604441, 1788035201, 10194593769, 58125109649, 331403923321, 1889520055201, 10773215969289, 61424160067249, 350213664213401, 1996764961336001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

First differences give {0, 8, 40, 232, 1320, 7528, 42920, ...} = 8*A015537(n) = 8 * {0, 1, 5, 29, 165, 941, 5365, ...}. - Alexander Adamchuk, Nov 03 2006

LINKS

Reinhard Zumkeller, 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^(n-k)*A122542(n,k) . G.f. (1-4*x)/(1-5*x-4*x^2)

a(n) = 1 + 8*Sum[ A015537(k), {k,0,n} ]. - Alexander Adamchuk, Nov 03 2006

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, 1}, 30] (* Harvey P. Dale, Jul 25 2011 *)

PROG

(Haskell)

a123270 n = a123270_list !! n

a123270_list = 1 : 1 : zipWith (-) (map (* 5) $

   zipWith (+) (tail a123270_list) a123270_list) a123270_list

-- Reinhard Zumkeller, Aug 16 2013

CROSSREFS

Cf. A015537.

Cf. A095344, A090390.

Sequence in context: A146798 A055428 A012231 * A114040 A231178 A090390

Adjacent sequences:  A123267 A123268 A123269 * A123271 A123272 A123273

KEYWORD

nonn

AUTHOR

Philippe Deléham, Oct 09 2006

STATUS

approved

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Last modified October 15 18:16 EDT 2019. Contains 328037 sequences. (Running on oeis4.)