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A173924
Expansion of 1/(1 - x^5 - x^6 - x^7 - x^8 + x^13).
23
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
Michael Mossinghoff, Small Salem Numbers
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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 26 2010
EXTENSIONS
More terms from Franck Maminirina Ramaharo, Nov 03 2018
STATUS
approved