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A015575 Expansion of x/(1-8x-5x^2). 3
0, 1, 8, 69, 592, 5081, 43608, 374269, 3212192, 27568881, 236612008, 2030740469, 17428983792, 149585572681, 1283829500408, 11018563866669, 94567658435392, 811634086816481, 6965910986708808, 59785458327752869, 513113221555566992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 2, 3, 2, 4, 6, 21, 4, 9, 4,120, 6, 56, 42, 12, 8, 16, 18,360, 4,... - 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 (8,5).

FORMULA

a(n) = 8 a(n-1) + 5 a(n-2).

a(n)=(1/42)*[4+sqrt(21)]^n*sqrt(21)-(1/42)*sqrt(21)*[4-sqrt(21)]^n, with n>=0 - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b+5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)

LinearRecurrence[{8, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 8, -5) for n in xrange(0, 20)]# [From Zerinvary Lajos, Apr 25 2009]

(MAGMA) [n le 2 select n-1 else 8*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

CROSSREFS

Sequence in context: A087487 A178368 A152279 * A214344 A228421 A152109

Adjacent sequences:  A015572 A015573 A015574 * A015576 A015577 A015578

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 20 15:14 EDT 2017. Contains 293612 sequences.