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A015541 Expansion of x/(1 - 5*x - 7*x^2). 3
0, 1, 5, 32, 195, 1199, 7360, 45193, 277485, 1703776, 10461275, 64232807, 394392960, 2421594449, 14868722965, 91294775968, 560554940595, 3441838134751, 21133075257920, 129758243232857, 796722742969725, 4891921417478624, 30036666288181195 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 3, 8, 6, 8, 24, 6, 6, 24, 24, 5, 24, 12, 6, 8, 12, 16, 24, 120, 24, ... - 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 (5,7).

FORMULA

a(n) = 5*a(n-1) + 7*a(n-2).

a(n) = (1/53)*sqrt(53)*((5/2 + (1/2)*sqrt(53))^n - (5/2 - (1/2)*sqrt(53))^n), with n >= 0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=5*b+7*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)

LinearRecurrence[{5, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

PROG

(Sage) [lucas_number1(n, 5, -7) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 5*Self(n-1) + 7*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-7*x^2))) \\ G. C. Greubel, Jan 24 2018

CROSSREFS

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.

Sequence in context: A157704 A270565 A271165 * A297068 A024064 A164594

Adjacent sequences:  A015538 A015539 A015540 * A015542 A015543 A015544

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 20 03:05 EDT 2019. Contains 328244 sequences. (Running on oeis4.)