cp's OEIS Frontend

A225499 Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).

%I A225499 #22 Sep 08 2022 08:46:05
%S A225499 1,1,0,0,1,1,1,2,2,2,3,4,4,5,7,9,11,13,16,20,25,31,39,48,59,74,92,113,
%T A225499 140,175,217,269,334,414,513,637,791,981,1217,1510,1874,2325,2884,
%U A225499 3578,4440,5509,6835,8481,10522,13054,16197,20097,24934,30936,38384
%N A225499 Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).
%C A225499 Limiting ratio is 1.24073..., the largest real root of 1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12: 1.240726423652541392056148161575
%C A225499 is a candidate for the smallest degree-12 Salem number.
%H A225499 G. C. Greubel, <a href="/A225499/b225499.txt">Table of n, a(n) for n = 0..1000</a>
%H A225499 Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A225499 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,0,0,1,0,0,1,-1,1,-1).
%F A225499 a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) + a(n-9) - a(n-10) + a(n-11) - a(n-12). - _Franck Maminirina Ramaharo_, Nov 02 2018
%t A225499 CoefficientList[Series[1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12), {x, 0, 50}], x]
%t A225499 LinearRecurrence[{1,-1,1,0,0,1,0,0,1,-1,1,-1},{1,1,0,0,1,1,1,2,2,2,3,4},100] (* _G. C. Greubel_, Nov 16 2016 *)
%o A225499 (PARI) Vec(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12) + O(x^50)) \\ _G. C. Greubel_, Nov 16 2016
%o A225499 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12))); // _G. C. Greubel_, Nov 03 2018
%Y A225499 Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482.
%K A225499 nonn,easy
%O A225499 0,8
%A A225499 _Roger L. Bagula_, May 09 2013