A173924 Expansion of 1/(1 - x^5 - x^6 - x^7 - x^8 + x^13).

1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 3, 3, 3, 3, 4, 6, 8, 10, 11, 12, 16, 20, 26, 32, 38, 46, 56, 70, 88, 108, 132, 161, 198, 244, 302, 372, 457, 561, 689, 849, 1046, 1287, 1584, 1947, 2395, 2947, 3627, 4464, 5492, 6756, 8312, 10227, 12584, 15484, 19052, 23440

Offset

0,12

Comments

Limiting ratio is: 1.2303914344072246.

Related to the 7th Salem on the Mossinghoff's list by factorization:

(1 + x)*(1 - x + x^2)*(1 - x^3 - x^5 - x^7 + x^10)

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

Formula

a(n) = a(n-5) + a(n-6) + a(n-7) + a(n-8) - a(n-13). - Franck Maminirina Ramaharo, Oct 30 2018

Maple

seq(coeff(series(1/(1-x^5-x^6-x^7-x^8+x^13), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 15 2019

Mathematica

CoefficientList[Series[1/(1-x^5-x^6-x^7-x^8+x^13), {x, 0, 50}], x]

Prog

(PARI) my(x='x+O('x^50)); Vec(1/(1-x^5-x^6-x^7-x^8+x^13)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^5-x^6-x^7-x^8+x^13))); // G. C. Greubel, Nov 03 2018
(Sage)
def A173924_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^5-x^6-x^7-x^8+x^13) ).list()
A173924_list(50) # G. C. Greubel, Dec 15 2019

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A364882 A029089 A358468 * A307392 A046886 A257246

Adjacent sequences: A173921 A173922 A173923 * A173925 A173926 A173927

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 26 2010

Extensions

More terms from Franck Maminirina Ramaharo, Nov 03 2018

Status

approved