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Expansion of 1/(1 + x - x^3 - x^4 - x^8 - x^12 - x^13 - x^17 - x^21 - x^22 - x^26 - x^30 - x^31 + x^33 + x^34).
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%I #23 Sep 08 2022 08:45:50

%S 1,-1,1,0,0,0,1,-1,2,-2,3,-2,3,-2,4,-3,6,-5,9,-7,12,-9,16,-12,22,-17,

%T 31,-24,43,-33,59,-45,81,-63,113,-88,156,-121,215,-168,298,-233,412,

%U -323,570,-448,788,-621,1090,-861,1507,-1193,2084,-1654,2882,-2293

%N Expansion of 1/(1 + x - x^3 - x^4 - x^8 - x^12 - x^13 - x^17 - x^21 - x^22 - x^26 - x^30 - x^31 + x^33 + x^34).

%C This polynomial is what I call a bi-Salem polynomial because it has two roots bigger than 1 (one positive and one negative).

%H G. C. Greubel, <a href="/A173908/b173908.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,-1,-1).

%F a(n) = a(n-1) + (n-3) + a(n-4) + a(n-8) + a(n-12) + a(n-13) + a(n-17) + a(n-21) + a(n-22) + a(n-26) + a(n-30) + a(n-31) - a(n-33) - a(n-34). - _Franck Maminirina Ramaharo_, Nov 02 2018

%p seq(coeff(series(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+ x^33+x^34), x, n+1), x, n), n = 0..60); # _G. C. Greubel_, Dec 15 2019

%t CoefficientList[Series[1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34), {x, 0, 60}], x]

%o (PARI) x='x+O('x^60); Vec(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26 - x^30-x^31+x^33+x^34)) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1+x-x^3 -x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+x^33+x^34))); // _G. C. Greubel_, Nov 03 2018

%o (Sage)

%o def A173908_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( 1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34) ).list()

%o A173908_list(30) # _G. C. Greubel_, Dec 15 2019

%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

%K sign,easy

%O 0,9

%A _Roger L. Bagula_, Nov 26 2010