%I #30 Sep 08 2022 08:46:05
%S 1,0,0,1,1,1,1,2,2,3,4,4,6,8,10,12,16,21,26,34,43,55,71,91,116,148,
%T 191,244,312,400,512,656,840,1076,1377,1764,2260,2893,3705,4745,6077,
%U 7782,9966,12763,16344,20932,26806,34328,43962,56300,72100,92333,118246
%N Expansion of 1/(1 - x^3 - x^4 - x^5 + x^8).
%C Limiting ratio is 1.28064..., the largest real root of 1 - x^3 - x^4 - x^5 + x^8: 1.280638156267757596701902532710 is a candidate for the smallest degree-8 Salem number.
%H G. C. Greubel, <a href="/A225482/b225482.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1,0,0,-1).
%F a(n) = a(n-3) + a(n-4) + a(n-5) - a(n-8). - _Franck Maminirina Ramaharo_, Nov 02 2018
%t CoefficientList[Series[1/(1 - x^3 - x^4 - x^5 + x^8), {x, 0, 50}], x]
%t LinearRecurrence[{0,0,1,1,1,0,0,-1}, {1,0,0,1,1,1,1,2}, 100] (* _G. C. Greubel_, Nov 16 2016 *)
%o (PARI) Vec(1/(1-x^3-x^4-x^5+x^8)+O(x^99)) \\ _Charles R Greathouse IV_, May 08 2013
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5+x^8))); // _G. C. Greubel_, Nov 03 2018
%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225499.
%K nonn,easy
%O 0,8
%A _Roger L. Bagula_, May 08 2013
%E More terms from _Franck Maminirina Ramaharo_, Nov 02 2018