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 A201838 #25 Apr 23 2024 11:07:38
%S A201838 0,1,1,-1,-3,-2,4,9,3,-15,-25,0,52,65,-27,-169,-155,158,520,321,-681,
%T A201838 -1519,-481,2560,4200,-79,-8839,-10881,4797,28638,25804,-27351,-87877,
%U A201838 -52895,116775,256000,76892,-436655,-705667,26871,1502085,1821118,-850160
%N A201838 G.f.: imaginary part of 1/(1 - i*x - i*x^2) where i=sqrt(-1).
%C A201838 The norm of the coefficients in 1/(1 - i*x - i*x^2) is given by A105309.
%H A201838 Paul D. Hanna, <a href="/A201838/b201838.txt">Table of n, a(n) for n = 0..500</a>
%H A201838 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,-2,-1).
%F A201838 G.f.: x*(1+x)/(1 + x^2*(1+x)^2).
%F A201838 a(n) = A201837(n-1) + A201837(n-2), where A201837 gives the real part of the coefficients in 1/(1 - i*x - i*x^2).
%F A201838 a(n) = Im((((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
%e A201838 G.f.: A(x) = x + x^2 - x^3 - 3*x^4 - 2*x^5 + 4*x^6 + 9*x^7 + 3*x^8 - 15*x^9 +...
%e A201838 A201837 gives the real part of coefficients in 1/(1 - i*x - i*x^2) and begins: 1, 0, -1, -2, 0, 4, 5, -2, -13, -12, 12, 40, 25, -52, -117, -38, 196, 324,... in which the pairwise sums generate this sequence.
%t A201838 LinearRecurrence[{0,-1,-2,-1},{0,1,1,-1},50] (* _Harvey P. Dale_, Apr 23 2024 *)
%o A201838 (PARI) {a(n)=imag(polcoeff(1/(1-I*x-I*x^2+x*O(x^n)),n))}
%o A201838 (PARI) {a(n)=polcoeff(x*(1+x)/(1 + x^2 + 2*x^3 + x^4 +x*O(x^n)), n)}
%Y A201838 Cf. A201837 (real), A105309 (norm).
%K A201838 sign,easy
%O A201838 0,5
%A A201838 _Paul D. Hanna_, Dec 06 2011