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A015580 Expansion of x/(1 - 9*x - 4*x^2). 3
0, 1, 9, 85, 801, 7549, 71145, 670501, 6319089, 59553805, 561260601, 5289560629, 49851088065, 469818035101, 4427766668169, 41729172153925, 393273616058001, 3706379233137709, 34930507562471385, 329200084994793301, 3102522795203025249, 29239505496806400445 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 1, 2, 1, 3, 2, 48, 2, 6, 3, 10, 2, 42, 48, 6, 4, 24, 6,360, 3, ... - R. J. Mathar, Aug 10 2012

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9,4)

FORMULA

a(n) = 9*a(n-1) + 4*a(n-2).

a(n) = (1/97)*sqrt(97)*{[(9/2) + (1/2)*sqrt(97)]^n - [(9/2) - (1/2)*sqrt(97)]^n}, with n>=0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b+4*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

LinearRecurrence[{9, 4}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 9, -4) for n in xrange(0, 19)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) [n le 2 select n-1 else 9*Self(n-1) + 4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-4*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Cf. A015579, A099371.

Sequence in context: A197197 A295118 A228417 * A163308 A160112 A108427

Adjacent sequences:  A015577 A015578 A015579 * A015581 A015582 A015583

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Extended by T. D. Noe, May 23 2011

STATUS

approved

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Last modified November 19 19:09 EST 2019. Contains 329323 sequences. (Running on oeis4.)