A175740 Expansion of 1/(1 - x - x^10 - x^19 + x^20).

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

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 (1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-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

Crossrefs

Cf. A175739.

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

Sequence in context: A064915 A180648 A322605 * A320321 A215009 A281943

Adjacent sequences: A175737 A175738 A175739 * A175741 A175742 A175743

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 04 2010

Status

approved