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 A153257 #19 Aug 28 2025 00:04:34
%S A153257 -1,-3,-1,11,39,89,167,279,431,629,879,1187,1559,2001,2519,3119,3807,
%T A153257 4589,5471,6459,7559,8777,10119,11591,13199,14949,16847,18899,21111,
%U A153257 23489,26039,28767,31679,34781,38079,41579,45287,49209,53351,57719,62319,67157,72239
%N A153257 a(n) = n^3 - (n+1)^2.
%H A153257 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A153257 From _Elmo R. Oliveira_, Aug 27 2025: (Start)
%F A153257 G.f.: (-1 + x + 5*x^2 + x^3)/(1 - x)^4.
%F A153257 E.g.f.: (-1 + x)*(1 + 3*x + x^2)*exp(x).
%F A153257 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t A153257 Table[n^3-(n+1)^2,{n,0,40}] (* _Harvey P. Dale_, Oct 05 2022 *)
%o A153257 (PARI) my(x='x+O('x^43)); Vec((x^3+5*x^2+x-1)/(x-1)^4) \\ _Elmo R. Oliveira_, Aug 27 2025
%Y A153257 Cf. A045991, A069778, A081437, A140719.
%K A153257 sign,easy,changed
%O A153257 0,2
%A A153257 _Vladimir Joseph Stephan Orlovsky_, Dec 22 2008
%E A153257 More terms from _Elmo R. Oliveira_, Aug 27 2025