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A015535 Expansion of x/(1-5*x-2*x^2). 14
0, 1, 5, 27, 145, 779, 4185, 22483, 120785, 648891, 3486025, 18727907, 100611585, 540513739, 2903791865, 15599986803, 83807517745, 450237562331, 2418802847145, 12994489360387, 69810052496225, 375039241201899, 2014816311001945, 10824160037413523 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths:  1, 1, 3, 2, 8, 3, 48, 2, 3, 8, 110, 6, 168, 48, 24, 4, 8, 3, 45, 8,... - R. J. Mathar, Aug 10 2012

This is the Lucas sequence U(5,-2). - Bruno Berselli, Jan 08 2013

LINKS

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

Wikipedia, Lucas sequence: Specific names.

Index to sequences with linear recurrences with constant coefficients, signature (5,2).

FORMULA

a(n) = 5*a(n-1) + 2*a(n-2) with n>1, a(0)=0, a(1)=1.

a(n) = (1/33)*sqrt(33)*(((5/2)+(1/2)*sqrt(33))^n-((5/2)-(1/2)*sqrt(33))^n). [Paolo P. Lava, Jan 13 2009]

MATHEMATICA

Join[{a=0, b=1}, Table[c=5*b+2*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011*)

LinearRecurrence[{5, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)

PROG

(Sage) [lucas_number1(n, 5, -2) for n in xrange(0, 22)]# [Zerinvary Lajos, Apr 24 2009]

(MAGMA) [n le 2 select n-1 else 5*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012

CROSSREFS

Cf. A201002 (prime subsequence)

Sequence in context: A037675 A221673 A052225 * A026292 A100193 A158869

Adjacent sequences:  A015532 A015533 A015534 * A015536 A015537 A015538

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 23 09:20 EST 2014. Contains 249840 sequences.