cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A166592 Hankel transform of A166588(n-1).

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%I A166592 #16 May 18 2016 12:03:16
%S A166592 0,1,3,2,3,1,0,-1,-3,-2,-3,-1,0,1,3,2,3,1,0,-1,-3,-2,-3,-1,0,1,3,2,3,
%T A166592 1,0,-1,-3,-2,-3,-1,0,1,3,2,3,1,0,-1,-3,-2,-3,-1,0,1,3,2,3,1,0,-1,-3,
%U A166592 -2,-3,-1,0,1,3,2,3,1,0,-1,-3,-2,-3,-1,0,1,3,2,3,1,0,-1,-3,-2,-3,-1,0,1,3
%N A166592 Hankel transform of A166588(n-1).
%C A166592 Hankel transform of 0,1,2,2,3,3,5,5,10,10,... is -a(n).
%H A166592 G. C. Greubel, <a href="/A166592/b166592.txt">Table of n, a(n) for n = 0..100</a>
%H A166592 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1).
%F A166592 G.f.: x(1+3x+x^2)/(1-x^2+x^4).
%F A166592 a(n) = (1-sqrt(3))*sin(5*Pi*n/6)+(1+sqrt(3))*sin(Pi*n/6).
%F A166592 From _G. C. Greubel_, May 18 2016: (Start)
%F A166592 a(n+12) = a(n).
%F A166592 a(n) = a(n-2) - a(n-4). (End)
%F A166592 E.g.f.: 2*sin(x/2)*(sqrt(3)*sinh(sqrt(3)*x/2) + cosh(sqrt(3)*x/2)). - _Ilya Gutkovskiy_, May 18 2016
%t A166592 CoefficientList[Series[x (1 + 3 x + x^2)/(1 - x^2 + x^4), {x, 0, 10}], x] (* or *) LinearRecurrence[{0,1,0,-1},{0,1,3,2}, 25] (* _G. C. Greubel_, May 18 2016 *)
%K A166592 easy,sign
%O A166592 0,3
%A A166592 _Paul Barry_, Oct 17 2009