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%I #21 Sep 08 2022 08:45:51
%S 1,0,0,0,0,1,1,1,1,0,1,2,3,3,3,3,4,6,8,10,11,12,16,20,26,32,38,46,56,
%T 70,88,108,132,161,198,244,302,372,457,561,689,849,1046,1287,1584,
%U 1947,2395,2947,3627,4464,5492,6756,8312,10227,12584,15484,19052,23440
%N Expansion of 1/(1 - x^5 - x^6 - x^7 - x^8 + x^13).
%C Limiting ratio is: 1.2303914344072246.
%C Related to the 7th Salem on the Mossinghoff's list by factorization:
%C (1 + x)*(1 - x + x^2)*(1 - x^3 - x^5 - x^7 + x^10)
%H G. C. Greubel, <a href="/A173924/b173924.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,1,1,1,0,0,0,0,-1).
%F a(n) = a(n-5) + a(n-6) + a(n-7) + a(n-8) - a(n-13). - _Franck Maminirina Ramaharo_, Oct 30 2018
%p seq(coeff(series(1/(1-x^5-x^6-x^7-x^8+x^13), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Dec 15 2019
%t CoefficientList[Series[1/(1-x^5-x^6-x^7-x^8+x^13), {x, 0, 50}], x]
%o (PARI) my(x='x+O('x^50)); Vec(1/(1-x^5-x^6-x^7-x^8+x^13)) \\ _G. C. Greubel_, Nov 03 2018
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^5-x^6-x^7-x^8+x^13))); // _G. C. Greubel_, Nov 03 2018
%o (Sage)
%o def A173924_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/(1-x^5-x^6-x^7-x^8+x^13) ).list()
%o A173924_list(50) # _G. C. Greubel_, Dec 15 2019
%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K nonn,easy
%O 0,12
%A _Roger L. Bagula_, Nov 26 2010
%E More terms from _Franck Maminirina Ramaharo_, Nov 03 2018
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