A225391 Expansion of 1/(1 - x - x^2 - x^6 + x^8).

1, 1, 2, 3, 5, 8, 14, 23, 38, 63, 104, 172, 285, 472, 781, 1293, 2140, 3542, 5863, 9705, 16064, 26590, 44013, 72852, 120588, 199603, 330392, 546880, 905221, 1498363, 2480159, 4105273, 6795236, 11247786, 18617851, 30817120, 51009909, 84433939, 139758925

Offset

0,3

Comments

Limiting ratio is 1.65525..., the largest real root of 1 - x^2 - x^6 - x^7 + x^8.

Links

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

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

Formula

a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-8). - Franck Maminirina Ramaharo, Nov 02 2018

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, 14, 23}, 100] (* 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, A225393, A225394, A225482, A225499.

Sequence in context: A282240 A004692 A094926 * A078843 A018068 A120400

Adjacent sequences: A225388 A225389 A225390 * A225392 A225393 A225394

Keyword

nonn,easy

Author

Roger L. Bagula, May 06 2013

Status

approved