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A175740
Expansion of 1/(1 - x - x^10 - x^19 + x^20).
23
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 21, 26, 32, 39, 47, 56, 66, 79, 94, 112, 134, 161, 194, 234, 282, 339, 407, 488, 585, 701, 840, 1007, 1208, 1450, 1741, 2090, 2510, 3013, 3616, 4339, 5206, 6246, 7494, 8992, 10790, 12948
OFFSET
0,11
COMMENTS
Limiting ratio is 1.2000265239873915.
LINKS
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-1).
FORMULA
G.f.: 1/((1 - x + x^2)*(1 - x^2 + x^4)*(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14)).
a(n) = a(n-1) + a(n-10) + a(n-19) + a(n-20). - Franck Maminirina Ramaharo, Oct 31 2018
MAPLE
seq(coeff(series(1/(1 -x -x^10 -x^19 +x^20), x, n+1), x, n), n = 0..60); # G. C. Greubel, Dec 05 2019
MATHEMATICA
CoefficientList[Series[1/(1 -x -x^10 -x^19 +x^20), {x, 0, 60}], x]
PROG
(PARI) my(x='x+O('x^60)); Vec(1/(1 -x -x^10 -x^19 +x^20)) \\ G. C. Greubel, Nov 03 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!(1/(1 - x - x^10 - x^19 + x^20))); // G. C. Greubel, Nov 03 2018
(Sage)
def A175740_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1 -x -x^10 -x^19 +x^20) ).list()
A175740_list(60) # G. C. Greubel, Dec 05 2019
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Dec 04 2010
STATUS
approved