A173925 Expansion of 1/(1 - x - x^8 - x^15 + x^16).

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 19, 24, 30, 37, 45, 56, 69, 85, 105, 130, 161, 199, 246, 304, 376, 465, 575, 711, 879, 1086, 1343, 1660, 2052, 2537, 3137, 3879, 4796, 5929, 7330, 9062, 11203, 13850, 17123, 21170, 26173, 32359, 40006

Offset

0,9

Comments

Limiting ratio is 1.2303914344072246.

The polynomial is the 10th Salem on Mossinghoff's list.

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 (1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,-1).

Formula

a(n) = a(n-1) + a(n-8) + a(n-15) - a(n-16). - Harvey P. Dale, Apr 02 2012

Maple

seq(coeff(series(1/(1-x-x^8-x^15+x^16), x, n+1), x, n), n = 0..60); # G. C. Greubel, Dec 15 2019

Mathematica

CoefficientList[Series[1/(1-x-x^8-x^15+x^16), {x, 0, 60}] , x] (* Harvey P. Dale, Apr 02 2012 *)

Prog

(PARI) my(x='x+O('x^60)); Vec(1/(1-x-x^8-x^15+x^16)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!(1/(1-x-x^8-x^15+x^16))); // G. C. Greubel, Nov 03 2018
(Sage)
def A173925_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x-x^8-x^15+x^16) ).list()
A173925_list(60) # G. C. Greubel, Dec 15 2019

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A266480 A246080 A278619 * A320319 A263363 A061920

Adjacent sequences: A173922 A173923 A173924 * A173926 A173927 A173928

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 26 2010

Status

approved