login
A173925
Expansion of 1/(1 - x - x^8 - x^15 + x^16).
23
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
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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Nov 26 2010
STATUS
approved