A225482 Expansion of 1/(1 - x^3 - x^4 - x^5 + x^8).

1, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 6, 8, 10, 12, 16, 21, 26, 34, 43, 55, 71, 91, 116, 148, 191, 244, 312, 400, 512, 656, 840, 1076, 1377, 1764, 2260, 2893, 3705, 4745, 6077, 7782, 9966, 12763, 16344, 20932, 26806, 34328, 43962, 56300, 72100, 92333, 118246

Offset

0,8

Comments

Limiting ratio is 1.28064..., the largest real root of 1 - x^3 - x^4 - x^5 + x^8: 1.280638156267757596701902532710 is a candidate for the smallest degree-8 Salem number.

Links

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

Michael Mossinghoff, Small Salem Numbers

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

Formula

a(n) = a(n-3) + a(n-4) + a(n-5) - a(n-8). - Franck Maminirina Ramaharo, Nov 02 2018

Mathematica

CoefficientList[Series[1/(1 - x^3 - x^4 - x^5 + x^8), {x, 0, 50}], x]
LinearRecurrence[{0, 0, 1, 1, 1, 0, 0, -1}, {1, 0, 0, 1, 1, 1, 1, 2}, 100] (* G. C. Greubel, Nov 16 2016 *)

Prog

(PARI) Vec(1/(1-x^3-x^4-x^5+x^8)+O(x^99)) \\ Charles R Greathouse IV, May 08 2013
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5+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, A225393, A225394, A225499.

Sequence in context: A325854 A301370 A342520 * A004056 A284334 A198317

Adjacent sequences: A225479 A225480 A225481 * A225483 A225484 A225485

Keyword

nonn,easy

Author

Roger L. Bagula, May 08 2013

Extensions

More terms from Franck Maminirina Ramaharo, Nov 02 2018

Status

approved