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A015581 a(n) = 9*a(n-1) + 5*a(n-2). 3
0, 1, 9, 86, 819, 7801, 74304, 707741, 6741189, 64209406, 611590599, 5825362421, 55486214784, 528502745161, 5033955780369, 47948115749126, 456702820643979, 4350065964541441, 41434107784092864, 394657299879542981, 3759086237836351149, 35805062639924875246 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A linear 2nd-order recurrence.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9,5).

FORMULA

G.f.: x/(1 - 9*x - 5*x^2). - R. J. Mathar, Dec 02 2007

a(n) = (1/101)*sqrt(101)*(((9/2) + (1/2)*sqrt(101))^n - ((9/2) - (1/2)*sqrt(101))^n). - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b+5*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

LinearRecurrence[{9, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

PROG

(Sage) [lucas_number1(n, 9, -5) for n in xrange(0, 19)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n le 2 select n-1 else 9*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-5*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Cf. A015579, A099371.

Sequence in context: A029711 A204465 A276242 * A152261 A028339 A180751

Adjacent sequences:  A015578 A015579 A015580 * A015582 A015583 A015584

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Extended by T. D. Noe, May 23 2011

STATUS

approved

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Last modified September 25 11:05 EDT 2018. Contains 315389 sequences. (Running on oeis4.)