A123270 a(0)=1, a(1)=1, a(n) = 5*a(n-1) + 4*a(n-2).

1, 1, 9, 49, 281, 1601, 9129, 52049, 296761, 1692001, 9647049, 55003249, 313604441, 1788035201, 10194593769, 58125109649, 331403923321, 1889520055201, 10773215969289, 61424160067249, 350213664213401, 1996764961336001

Offset: 0

Author

Philippe Deléham, Oct 09 2006

Keywords

• nonn

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
• Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
• Index entries for linear recurrences with constant coefficients, signature (5, 4).

Crossrefs

Cf. A015537.

Cf. A095344, A090390.

Programs

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

Mathematica

LinearRecurrence[{5,4},{1,1},30] (* Harvey P. Dale, Jul 25 2011 *)

Formula

a(n) = Sum_{k=0..n} 4^(n-k)*A122542(n,k).

G.f.: (1-4*x)/(1-5*x-4*x^2).

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