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%I #38 Sep 08 2022 08:44:50
%S 1,-1,1,0,0,1,0,1,0,1,1,1,1,2,1,2,3,2,4,3,5,5,6,8,8,10,12,14,16,20,22,
%T 27,31,37,44,50,61,70,83,98,115,135,159,187,220,259,304,359,420,496,
%U 583,685,807,948,1116,1312,1544
%N Expansion of 1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1) (inverse of Salem polynomial).
%C The root 1.1762808182599175065440703384740350... is the smallest known Salem number (A073011).
%H Simon Plouffe, <a href="/A029826/b029826.txt">Table of n, a(n) for n = 0..2998</a>
%H Leonard Lewin, <a href="https://bookstore.ams.org/surv-37">Structural Properties of Polylogarithms</a>, AMS #37. p. 365, 1991.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,1,1,1,0,-1,-1).
%F a(n) = -a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) - a(n-9) - a(n-10). - _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008
%t LinearRecurrence[{-1,0,1,1,1,1,1,0,-1,-1}, {1,-1,1,0,0,1,0,1,0,1}, 100] (* _G. C. Greubel_, May 07 2018 *)
%o (PARI) Vec(1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1)+O(x^66)) \\ _Joerg Arndt_, May 01 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1))); // _G. C. Greubel_, May 07 2018
%Y Cf. A073011, A125950.
%K sign,easy
%O 0,14
%A _Simon Plouffe_
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