A225394 Expansion of 1/(1 - x - x^2 + x^7 - x^9).

1, 1, 2, 3, 5, 8, 13, 20, 32, 51, 81, 129, 205, 326, 519, 826, 1314, 2091, 3327, 5294, 8424, 13404, 21328, 33937, 54000, 85924, 136721, 217548, 346159, 550803, 876429, 1394560, 2219002, 3530841, 5618219, 8939622, 14224586, 22633938, 36014767, 57306132, 91184618

Offset

0,3

Comments

Limiting ratio is 1.59118..., the largest real root of -1 + x^2 - x^7 - x^8 + x^9 = 0.

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,-1,0,1).

Formula

a(n) = a(n-1) + a(n-2) - a(n-7) + a(n-9). - Ilya Gutkovskiy, Nov 16 2016

Mathematica

CoefficientList[Series[1/(1 - x - x^2 + x^7 - x^9), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 0, 0, 0, -1, 0, 1}, {1, 1, 2, 3, 5, 8, 13, 20, 32}, 50] (* G. C. Greubel, Nov 16 2016 *)

Prog

(PARI) Vec(1/(1-x-x^2+x^7-x^9) + 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^7-x^9))); // 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, A181600, A204631, A225391, A225393, A225482, A225499.

Sequence in context: A055805 A023437 A322332 * A013985 A092834 A080106

Adjacent sequences: A225391 A225392 A225393 * A225395 A225396 A225397

Keyword

nonn,easy

Author

Roger L. Bagula, May 06 2013

Status

approved