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A161007 a(n+1) = 2*a(n) + 16*a(n-1), a(0)=0, a(1)=1. 3
0, 1, 2, 20, 72, 464, 2080, 11584, 56448, 298240, 1499648, 7771136, 39536640, 203411456, 1039409152, 5333401600, 27297349632, 139929124864, 716615843840, 3672097685504, 18810048872448, 96373660712960, 493708103385088, 2529394778177536, 12958119210516480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1)/a(n) = 1 + Sqrt(17) for large values on n.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,16).

FORMULA

a(n) = ((1+sqrt(17))^n - (1-sqrt(17))^n)/(2*sqrt(17)).

G.f.: -x / (16*x^2+2*x-1). - Colin Barker, Jul 01 2015

a(n) = 2^(n-1)*A006131(n-1). - R. J. Mathar, Mar 08 2021

MATHEMATICA

LinearRecurrence[{2, 16}, {0, 1}, 50] (* T. D. Noe, Nov 07 2011 *)

PROG

(PARI) concat(0, Vec(-x/(16*x^2+2*x-1) + O(x^40))) \\ Colin Barker, Jul 01 2015

CROSSREFS

Sequence in context: A003283 A259110 A135188 * A331760 A098077 A279264

Adjacent sequences:  A161004 A161005 A161006 * A161008 A161009 A161010

KEYWORD

nonn,easy

AUTHOR

Sture Sjöstedt, Jun 02 2009

STATUS

approved

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Last modified April 17 11:08 EDT 2021. Contains 343064 sequences. (Running on oeis4.)