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 A100133 #17 Feb 03 2023 01:37:22
%S A100133 1,2,4,8,19,50,136,368,985,2618,6940,18392,48763,129338,343120,910304,
%T A100133 2415025,6406898,16996852,45090728,119620579,317340098,841868632,
%U A100133 2233386320,5924932489,15718204970,41698695820,110622122360
%N A100133 a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 3^k * 2^(n-4k).
%C A100133 Binomial transform of 1,1,1,1,4,4,10,10,28,28,76,... (g.f. (1-x)(1+x)^2/(1-2x^2-2x^4)).
%H A100133 Seiichi Manyama, <a href="/A100133/b100133.txt">Table of n, a(n) for n = 0..1000</a>
%H A100133 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,0,3)
%F A100133 G.f.: (1-2x)/((1-2x)^2-3x^4).
%F A100133 a(n) = 4*a(n-1) - 4*a(n-2) + 3*a(n-4). [corrected by _Kevin Ryde_, Feb 02 2023]
%o A100133 (PARI) a(n) = sum(k=0, n\4, binomial(n-2*k,2*k) * 3^k * 2^(n-4*k)); \\ _Michel Marcus_, Oct 09 2021
%o A100133 (PARI) my(p=Mod('x, 'x^4-4*'x^3+4*'x^2-3)); a(n) = subst(lift(p^n),'x,2); \\ _Kevin Ryde_, Feb 02 2023
%Y A100133 Cf. A100131, A100132.
%K A100133 easy,nonn
%O A100133 0,2
%A A100133 _Paul Barry_, Nov 06 2004