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A015537 Expansion of x/(1 - 5*x - 4*x^2). 13
0, 1, 5, 29, 165, 941, 5365, 30589, 174405, 994381, 5669525, 32325149, 184303845, 1050819821, 5991314485, 34159851709, 194764516485, 1110461989261, 6331368012245, 36098688018269, 205818912140325, 1173489312774701, 6690722212434805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

First differences give A122690(n) = {1, 4, 24, 136, 776, 4424, 25224, ...}. Partial sums of a(n) are {0, 1, 6, 35, 200, ...} = (A123270(n) - 1)/8. - Alexander Adamchuk, Nov 03 2006

For n >= 2, a(n) equals the permanent of the (n-1) X (n-1) tridiagonal matrix with 5's along the main diagonal, and 2's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 19 2011

Pisano period lengths:  1, 1, 8, 1, 4, 8, 48, 1, 24, 4, 40, 8, 42, 48, 8, 2, 72, 24, 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 (5,4).

FORMULA

a(n) = 5*a(n-1) + 4*a(n-2).

a(n) = Sum_{k=0..floor((n-1)/2)} C(n-k-1, k)*4^k*5^(n-2*k-1). - Paul Barry, Apr 23 2005

a(n) = Sum_{k=0..(n-1)} A122690(k). - Alexander Adamchuk, Nov 03 2006

a(n) = (1/41)*sqrt(41)*((5/2 + (1/2)*sqrt(41))^n - (5/2 - (1/2)*sqrt(41))^n), with n >= 0. - Paolo P. Lava, Jan 13 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=5*b+4*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)

LinearRecurrence[{5, 4}, {0, 1}, 30] (* Vincenzo Librandi, Nov 12 2012 *)

PROG

(Sage) [lucas_number1(n, 5, -4) for n in xrange(0, 22)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 5*Self(n-1)+4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 12 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-4*x^2))) \\ G. C. Greubel, Jan 01 2018

CROSSREFS

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A122690, A123270, A180222, A180226.

Sequence in context: A272940 A146178 A272751 * A182017 A291017 A141812

Adjacent sequences:  A015534 A015535 A015536 * A015538 A015539 A015540

KEYWORD

nonn,easy,changed

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 19 09:50 EDT 2018. Contains 312774 sequences. (Running on oeis4.)