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 A368377 #16 Jul 26 2025 14:39:19
%S A368377 0,0,0,0,1,0,2,0,6,1,15,4,37,14,91,44,222,129,541,364,1319,1000,3219,
%T A368377 2696,7869,7172,19273,18892,47299,49398,116317,128444,286624,332552,
%U A368377 707679,858168,1750588,2208898,4338314,5674380,10769893,14554398,26780522,37286820
%N A368377 Arises from enumeration of a certain class of zig-zag knight's paths on the square grid.
%C A368377 It would be nice to have a more precise definition.
%H A368377 Jean-Luc Baril and José L. Ramírez, <a href="http://jl.baril.u-bourgogne.fr/knight.pdf">Knight's paths towards Catalan numbers</a>, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087 [math.CO], Jan 2023. See Section 2.2.
%F A368377 G.f.: (x + x^2 * R(x) + R(x)^2) * R(x)^2 / x^3 = F(x) * R(x), where R(x) = x * (A(x^2) - 1), A(x) is the g.f. of A004148, and F(x) is the g.f. of A368376. - _Andrei Zabolotskii_, Jul 25 2025
%t A368377 r = (1 - z^4 - z^2 - Sqrt[z^8 - 2z^6 - z^4 - 2z^2 + 1]) / (2z^3);
%t A368377 gf = r (u^2 z + u z^2 + 1) / (z^3 (1 - r u));
%t A368377 Table[SeriesCoefficient[gf,{u,0,3},{z,0,n}], {n,0,50}] (* _Andrei Zabolotskii_, Jul 25 2025 *)
%Y A368377 Cf. A144366, A368376.
%K A368377 nonn
%O A368377 0,7
%A A368377 _N. J. A. Sloane_, Feb 18 2024
%E A368377 Terms a(16) and beyond from _Andrei Zabolotskii_, Jul 25 2025