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A015525 Expansion of x/(1-3*x-8*x^2). 21
0, 1, 3, 17, 75, 361, 1683, 7937, 37275, 175321, 824163, 3875057, 18218475, 85655881, 402715443, 1893393377, 8901903675, 41852858041, 196773803523, 925144274897, 4349623252875, 20450023957801, 96147057896403 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,8).

FORMULA

a(n) = 3*a(n-1) + 8*a(n-2).

a(n) = -16^n*(A^n-B^n)/sqrt(41) where A = -1/(3+sqrt(41)) and B = 1/(sqrt(41)-3). - R. J. Mathar, Apr 29 2008

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 4}, {1, -4}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)

LinearRecurrence[{3, 8}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)

PROG

(Sage) [lucas_number1(n, 3, -8) for n in xrange(0, 23)]# Zerinvary Lajos, Apr 22 2009

(MAGMA) [n le 2 select n-1 else 3*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x-8*x^2))) \\ G. C. Greubel, Jan 01 2017

CROSSREFS

Sequence in context: A142868 A171875 A100233 * A062224 A217958 A093568

Adjacent sequences:  A015522 A015523 A015524 * A015526 A015527 A015528

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 23 20:17 EDT 2019. Contains 328373 sequences. (Running on oeis4.)