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 A357533 #26 Nov 25 2022 06:31:58
%S A357533 1,1,1,1,2,3,4,5,8,13,20,29,46,77,128,205,338,581,1012,1733,2990,5293,
%T A357533 9536,17117,30778,56165,104108,193621,360662,677693,1289080,2467373,
%U A357533 4735826,9142837,17814308,34950245,68835118,136197581,271384112,544302973,1096578410,2218459013,4513377436
%N A357533 a(n) = Sum_{k=0..floor(n/4)} (n-3*k)!/(n-4*k)!.
%H A357533 Seiichi Manyama, <a href="/A357533/b357533.txt">Table of n, a(n) for n = 0..1000</a>
%F A357533 a(n) = (3 * a(n-1) + n * a(n-4) + 1)/4 for n > 3.
%o A357533 (PARI) a(n) = sum(k=0, n\4, (n-3*k)!/(n-4*k)!);
%Y A357533 Cf. A072374, A122852, A357532, A357570.
%K A357533 nonn,easy
%O A357533 0,5
%A A357533 _Seiichi Manyama_, Nov 19 2022