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A015545 Expansion of x/(1 - 5*x - 9*x^2). 2
0, 1, 5, 34, 215, 1381, 8840, 56629, 362705, 2323186, 14880275, 95310049, 610472720, 3910154041, 25045024685, 160416509794, 1027487771135, 6581187443821, 42153327159320, 269997322790989, 1729366558388825, 11076808697063026, 70948342510814555 (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 (5,9).

FORMULA

a(n) = 5*a(n-1) + 9*a(n-2).

a(n) = (1/61)*sqrt(61)*(((5/2) + (1/2)*sqrt(61))^n - ((5/2) - (1/2)*sqrt(61))^n), with n>=0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 3}, {1, -6}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)

LinearRecurrence[{5, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

PROG

(Sage) [lucas_number1(n, 5, -9) for n in range(0, 21)]# Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 5*Self(n-1) + 9*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-9*x^2))) \\ G. C. Greubel, Jan 24 2018

CROSSREFS

Sequence in context: A076708 A127816 A024063 * A102436 A291027 A033889

Adjacent sequences:  A015542 A015543 A015544 * A015546 A015547 A015548

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)