A225393 Expansion of 1/(1 - x - x^2 + x^6 - x^8).

1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 74, 116, 183, 288, 453, 713, 1122, 1766, 2779, 4373, 6882, 10830, 17043, 26820, 42206, 66419, 104522, 164484, 258845, 407339, 641021, 1008761, 1587466, 2498162, 3931305, 6186612, 9735741, 15320931, 24110227, 37941757, 59708145

Offset

0,3

Links

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

Mohammed L. Nadji, Moussa Ahmia, Daniel F. Checa, and José L. Ramírez, Arndt Compositions with Restricted Parts, Palindromes, and Colored Variants, J. Int. Seq. (2025) Vol. 28, Issue 3, Article 25.3.6. See p. 8.

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

Formula

G.f.: 1/(1 - x - x^2 + x^6 - x^8).

a(n) = a(n-1) + a(n-2) - a(n-6) + a(n-8). - Ilya Gutkovskiy, Nov 16 2016

Mathematica

CoefficientList[Series[1/(1 - x - x^2 + x^6 - x^8), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 0, 0, -1, 0, 1}, {1, 1, 2, 3, 5, 8, 12, 19}, 50] (* G. C. Greubel, Nov 16 2016 *)

Prog

(PARI) Vec(1/(1-x-x^2+x^6-x^8) + 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^6-x^8))); // 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, A225394, A225482, A225499.

Sequence in context: A024567 A303668 A060961 * A243850 A357519 A179018

Adjacent sequences: A225390 A225391 A225392 * A225394 A225395 A225396

Keyword

nonn,easy

Author

Roger L. Bagula, May 06 2013

Status

approved