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Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.
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%I #25 Sep 08 2022 08:45:37

%S 1,0,0,1,0,1,1,1,2,1,2,3,3,4,5,6,7,9,11,14,17,20,26,31,38,48,58,72,88,

%T 108,134,164,202,249,306,376,463,570,701,863,1061,1306,1607,1976,2433,

%U 2993,3682,4531,5574,6859,8439,10383,12776,15719,19340,23796

%N Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.

%C The ratio productive positive root is 1.2303914344072246.

%H G. C. Greubel, <a href="/A143472/b143472.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,1,0,1,0,0,-1).

%F G.f.: 1/(1 - x^3 - x^5 - x^7 + x^10). - _Colin Barker_, Oct 23 2013

%F a(n) = a(n-3) + a(n-5) + a(n-7) - a(n-10). - _Franck Maminirina Ramaharo_, Oct 30 2018

%t CoefficientList[Series[1/(1 - x^3 - x^5 - x^7 + x^10), {x, 0, 50}], x]

%o (Maxima) makelist(ratcoef(taylor(1/(1 - x^3 - x^5 - x^7 + x^10), x, 0, n), x, n), n, 0, 50); /* _Franck Maminirina Ramaharo_, Nov 02 2018 */

%o (PARI) x='x+O('x^50); Vec(1/(1-x^3-x^5-x^7+x^10)) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^5-x^7+x^10))); // _G. C. Greubel_, Nov 03 2018

%Y Cf. A029826, A117791, A143419, A143438, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

%K nonn,easy

%O 0,9

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 24 2008

%E More terms from _Colin Barker_, Oct 23 2013

%E New name after _Colin Barker_'s formula by _Franck Maminirina Ramaharo_, Nov 03 2018