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

%I A175740 #24 Sep 08 2022 08:45:51
%S A175740 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,
%T A175740 79,94,112,134,161,194,234,282,339,407,488,585,701,840,1007,1208,1450,
%U A175740 1741,2090,2510,3013,3616,4339,5206,6246,7494,8992,10790,12948
%N A175740 Expansion of 1/(1 - x - x^10 - x^19 + x^20).
%C A175740 Limiting ratio is 1.2000265239873915.
%H A175740 G. C. Greubel, <a href="/A175740/b175740.txt">Table of n, a(n) for n = 0..1000</a>
%H A175740 Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A175740 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,-1).
%F A175740 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)).
%F A175740 a(n) = a(n-1) + a(n-10) + a(n-19) + a(n-20). - _Franck Maminirina Ramaharo_, Oct 31 2018
%p A175740 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
%t A175740 CoefficientList[Series[1/(1 -x -x^10 -x^19 +x^20), {x, 0, 60}], x]
%o A175740 (PARI) my(x='x+O('x^60)); Vec(1/(1 -x -x^10 -x^19 +x^20)) \\ _G. C. Greubel_, Nov 03 2018
%o A175740 (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!(1/(1 - x - x^10 - x^19 + x^20))); // _G. C. Greubel_, Nov 03 2018
%o A175740 (Sage)
%o A175740 def A175740_list(prec):
%o A175740     P.<x> = PowerSeriesRing(ZZ, prec)
%o A175740     return P( 1/(1 -x -x^10 -x^19 +x^20) ).list()
%o A175740 A175740_list(60) # _G. C. Greubel_, Dec 05 2019
%Y A175740 Cf. A175739.
%Y A175740 Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K A175740 nonn,easy
%O A175740 0,11
%A A175740 _Roger L. Bagula_, Dec 04 2010