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 A201837 #27 Sep 05 2022 19:56:21
%S A201837 1,0,-1,-2,0,4,5,-2,-13,-12,12,40,25,-52,-117,-38,196,324,-3,-678,
%T A201837 -841,360,2200,2000,-2079,-6760,-4121,8918,19720,6084,-33435,-54442,
%U A201837 1547,115228,140772,-63880,-372775,-332892,359763,1142322,678796,-1528956,-3323203
%N A201837 G.f.: real part of 1/(1 - i*x - i*x^2) where i=sqrt(-1).
%C A201837 The norm of the coefficients in 1/(1 - i*x - i*x^2) is given by A105309.
%H A201837 Paul D. Hanna, <a href="/A201837/b201837.txt">Table of n, a(n) for n = 0..500</a>
%H A201837 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,-2,-1).
%F A201837 G.f.: 1/(1 + x^2*(1+x)^2).
%F A201837 a(n) = -(A201838(n-1) + A201838(n-2)), where A201838 gives the imaginary part of the coefficients in 1/(1 - i*x - i*x^2).
%F A201837 a(n) = Re((((i + sqrt(4*i-1))^(n+1) - (i - sqrt(4*i-1))^(n+1)))/(2^(n+1)*sqrt(4*i-1))), where i=sqrt(-1). - _Daniel Suteu_, Apr 20 2018
%F A201837 a(n) = - a(n-2) - 2*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Sep 05 2022
%e A201837 G.f.: A(x) = 1 - x^2 - 2*x^3 + 4*x^5 + 5*x^6 - 2*x^7 - 13*x^8 - 12*x^9 +...
%e A201837 A201838 gives the imaginary part of coefficients in 1/(1 -i*x - i*x^2) and begins: 0, 1, 1, -1, -3, -2, 4, 9, 3, -15, -25, 0, 52, 65, -27, -169, -155, 158, 520,... in which this sequence equals the negative of the pairwise sums of A201838.
%t A201837 Re/@ CoefficientList[Series[1/(1-I*x-I*x^2),{x,0,50}],x] (* _Harvey P. Dale_, Dec 10 2011 *)
%o A201837 (PARI) {a(n)=real(polcoeff(1/(1-I*x-I*x^2+x*O(x^n)),n))}
%o A201837 (PARI) {a(n)=polcoeff(1/(1 + x^2 + 2*x^3 + x^4 +x*O(x^n)),n)}
%Y A201837 Cf. A201838 (imag), A105309 (norm).
%K A201837 sign,easy
%O A201837 0,4
%A A201837 _Paul D. Hanna_, Dec 06 2011