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 A279231 #33 Aug 03 2025 18:16:48
%S A279231 1,5,15,34,62,90,91,11,-231,-716,-1444,-2172,-2171,17,6579,19702,
%T A279231 39386,59070,59071,23,-177123,-531416,-1062856,-1594296,-1594295,29,
%U A279231 4782999,14348938,28697846,43046754,43046755,35,-129140127,-387420452,-774840940,-1162261428
%N A279231 Expansion of g.f. 1/((1 - x)^2*(1 - 3*x + 3*x^2)).
%H A279231 Colin Barker, <a href="/A279231/b279231.txt">Table of n, a(n) for n = 0..1000</a>
%H A279231 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,9,-3).
%F A279231 a(n) = 5*a(n-1) - 10*a(n-2) + 9*a(n-3) - 3*a(n-4) for n > 3.
%F A279231 a(n) = 3*a(n-1) - 3*a(n-2) + n + 1, with a(-1) = a(-2) = 0.
%F A279231 a(n) = 4 + n + 3^(1+n/2)*(sqrt(3)*sin(n*Pi/6) - cos(n*Pi/6)). - _Stefano Spezia_, Feb 11 2023
%F A279231 a(n) = Sum_{k=0..floor(n/3)} (-1)^k*binomial(n+4,3*k+4). - _Taras Goy_, Jan 03 2025
%F A279231 E.g.f.: exp(x)*(4 + x - 3*exp(x/2)*(cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))). - _Stefano Spezia_, Jan 03 2025
%t A279231 CoefficientList[Series[1/((1-x)^2(1-3x+3x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,9,-3},{1,5,15,34},40] (* _Harvey P. Dale_, Aug 03 2025 *)
%o A279231 (PARI) Vec(1/((1-x)^2*(1-3*x+3*x^2)) + O(x^30)) \\ _Colin Barker_, Dec 08 2016
%Y A279231 Cf. A001477, A045618, A077859.
%K A279231 sign,easy
%O A279231 0,2
%A A279231 _Philippe Deléham_, Dec 08 2016
%E A279231 Incorrect term corrected by _Colin Barker_, Dec 09 2016