A225499 - OEIS

A225499

Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).

1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 9, 11, 13, 16, 20, 25, 31, 39, 48, 59, 74, 92, 113, 140, 175, 217, 269, 334, 414, 513, 637, 791, 981, 1217, 1510, 1874, 2325, 2884, 3578, 4440, 5509, 6835, 8481, 10522, 13054, 16197, 20097, 24934, 30936, 38384

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,8

COMMENTS

Limiting ratio is 1.24073..., the largest real root of 1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12: 1.240726423652541392056148161575

is a candidate for the smallest degree-12 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 (1,-1,1,0,0,1,0,0,1,-1,1,-1).

FORMULA

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) + a(n-9) - a(n-10) + a(n-11) - a(n-12). - Franck Maminirina Ramaharo, Nov 02 2018

MATHEMATICA

CoefficientList[Series[1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12), {x, 0, 50}], x]

LinearRecurrence[{1, -1, 1, 0, 0, 1, 0, 0, 1, -1, 1, -1}, {1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4}, 100] (* G. C. Greubel, Nov 16 2016 *)

PROG

(PARI) Vec(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12) + 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^3 -x^6 -x^9 +x^10 -x^11 +x^12))); // 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, A225482.

Sequence in context: A338826 A274201 A079398 * A215473 A071988 A301337

Adjacent sequences: A225496 A225497 A225498 * A225500 A225501 A225502

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, May 09 2013

STATUS

approved