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.
%I A106202 #22 Jan 03 2016 03:52:00
%S A106202 0,0,0,2,4,6,8,2,-20,-66,-144,-230,-236,22,856,2610,5308,7918,7104,
%T A106202 -4150,-36636,-100794,-193368,-269342,-198772,274974,1522192,3846778,
%U A106202 6966452,8986230,4917240,-14538862,-61860772,-145127602,-248063392,-292843734,-90180988,692992166,2468418888,5415220546,8722746156,9258303102
%N A106202 Expansion of Im(x/(1 - x - 2*i*x^2)), i=sqrt(-1).
%C A106202 Real part is A106201.
%C A106202 For n>=2, a(n) equals -1 times the imaginary part of the determinant of the (n-1) X (n-1) matrix with i's along the superdiagonal (i is the imaginary unit), 2's along the subdiagonal, 1's along the main diagonal, and 0's everywhere else (see Mathematica code below). - _John M. Campbell_, Jun 04 2011
%H A106202 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,-4).
%F A106202 G.f.: 2*x^3/(1-2*x+x^2+4*x^4).
%F A106202 a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k)*2^k*sin(Pi*k/2).
%t A106202 Table[-Im[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {n - 1, n - 1}] + Array[KroneckerDelta[#1 - 1, #2]*2 &, {n - 1, n - 1}] + IdentityMatrix[n - 1]]], {n, 2, 40}] (* _John M. Campbell_, Jun 04 2011 *)
%o A106202 (PARI) concat(vector(3), Vec(2*x^3/(1-2*x+x^2+4*x^4) + O(x^50))) \\ _Michel Marcus_, Jan 03 2016
%Y A106202 Cf. A001045, A014292, A104862.
%K A106202 easy,sign
%O A106202 0,4
%A A106202 _Paul Barry_, Apr 25 2005