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 A128019 #18 Jun 09 2025 10:18:40
%S A128019 1,-3,-3,9,9,-27,-27,81,81,-243,-243,729,729,-2187,-2187,6561,6561,
%T A128019 -19683,-19683,59049,59049,-177147,-177147,531441,531441,-1594323,
%U A128019 -1594323,4782969,4782969,-14348907,-14348907,43046721,43046721,-129140163,-129140163,387420489,387420489
%N A128019 Expansion of (1 - 3x)/(1 + 3*x^2).
%H A128019 Harvey P. Dale, <a href="/A128019/b128019.txt">Table of n, a(n) for n = 0..1000</a>
%H A128019 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,-3)
%F A128019 a(n) = 3^floor((n+1)/2)*(-1)^C(n+1,2).
%F A128019 Binomial transform is A128018.
%F A128019 E.g.f.: cos(sqrt(3)*x) - sqrt(3)*sin(sqrt(3)*x). - _Stefano Spezia_, Dec 31 2022
%t A128019 CoefficientList[Series[(1 - 3x)/(1 + 3*x^2),{x,0,40}],x] (* _Stefano Spezia_, Dec 31 2022 *)
%t A128019 LinearRecurrence[{0,-3},{1,-3},40] (* _Harvey P. Dale_, Jun 09 2025 *)
%Y A128019 Cf. A108411, A128018.
%K A128019 easy,sign
%O A128019 0,2
%A A128019 _Paul Barry_, Feb 11 2007