A181600 Expansion of 1/(1 - x - x^2 + x^8 - x^10).

1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 85, 136, 218, 349, 559, 895, 1434, 2297, 3679, 5893, 9439, 15119, 24217, 38790, 62132, 99520, 159407, 255331, 408978, 655083, 1049283, 1680695, 2692063, 4312028, 6906816, 11063033, 17720278, 28383559, 45463532, 72821479

Offset

0,3

Comments

Limiting ratio is 1.60176..., the largest real root of -1 + x^2 - x^8 - x^9 + x^10. Compare this constant to Lehmer's Salem constant A073011 and the golden mean.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,0,0,-1,0,1).

Formula

a(n) = a(n-1) + a(n-2) - a(n-8) + a(n-10). - Franck Maminirina Ramaharo, Oct 31 2018

Mathematica

CoefficientList[Series[1/(1 - x - x^2 + x^8 - x^10), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 1, 2, 3, 5, 8, 13, 21, 33, 53}, 50] (* Harvey P. Dale, Aug 11 2015 *)

Prog

(PARI) Vec(1/(1 -x -x^2 +x^8 -x^10) + O(x^50)) \\ G. C. Greubel, Nov 16 2016
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x-x^2+x^8-x^10))); // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A358902 A023438 A117760 * A111917 A309676 A280198

Adjacent sequences: A181597 A181598 A181599 * A181601 A181602 A181603

Keyword

nonn,easy

Author

Roger L. Bagula, May 06 2013

Status

approved