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 A305291 #31 Jun 04 2018 18:41:02
%S A305291 -1,6,-32,85,-183,332,-550,843,-1229,1714,-2316,3041,-3907,4920,-6098,
%T A305291 7447,-8985,10718,-12664,14829,-17231,19876,-22782,25955,-29413,33162,
%U A305291 -37220,41593,-46299,51344,-56746,62511,-68657,75190,-82128,89477,-97255,105468,-114134,123259,-132861
%N A305291 Numbers k such that 4*k + 3 is a perfect cube, sorted by absolute values.
%H A305291 Colin Barker, <a href="/A305291/b305291.txt">Table of n, a(n) for n = 1..1000</a>
%H A305291 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-2,2,3,1).
%F A305291 G.f.: x*(-1 + 3*x - 16*x^2 + 3*x^3 - x^4)/((1 - x)*(1 + x)^4).
%F A305291 a(n) = -3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5).
%F A305291 a(n) = (-3 + A016755(n-1)*(-1)^n)/4.
%F A305291 a(n) = -A305290(n) - 1.
%F A305291 a(n) + a(-n) = 1 - 2^(1+(-1)^n).
%F A305291 (n - 2)*(4*n^2 - 16*n + 19)*a(n) + (12*n^2 - 36*n + 31)*a(n-1) - (n - 1)*(4*n^2 - 8*n + 7)*a(n-2) = 0.
%F A305291 From _Colin Barker_, May 30 2018: (Start)
%F A305291 a(n) = (4*n^3 - 6*n^2 + 3*n - 2)/2 for n even.
%F A305291 a(n) = -(4*n^3 - 6*n^2 + 3*n + 1)/2 for n odd.
%F A305291 (End)
%p A305291 seq(coeff(series(x*(-1+3*x-16*x^2+3*x^3-x^4)/((1-x)*(1+x)^4), x,50),x,n),n=1..45); # _Muniru A Asiru_, May 31 2018
%t A305291 LinearRecurrence[{-3, -2, 2, 3, 1}, {-1, 6, -32, 85, -183}, 45] (* _Jean-François Alcover_, Jun 04 2018 *)
%o A305291 (PARI) Vec(-x*(1 - 3*x + 16*x^2 - 3*x^3 + x^4) / ((1 - x)*(1 + x)^4) + O(x^40)) \\ _Colin Barker_, Jun 04 2018
%Y A305291 Cf. A016755, A305290.
%K A305291 sign,easy
%O A305291 1,2
%A A305291 _Bruno Berselli_, May 29 2018