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 A368376 #20 Jul 26 2025 14:38:50
%S A368376 0,1,0,1,0,3,1,6,3,13,9,29,25,65,66,148,171,341,437,793,1107,1860,
%T A368376 2790,4395,7009,10452,17574,24999,44019,60097,110210,145130,275925,
%U A368376 351916,690993,856502,1731224,2091599,4339980,5123437,10887192,12585354,27331465
%N A368376 Arises from enumeration of a certain class of zig-zag knight's paths on the square grid.
%C A368376 It would be nice to have a more precise definition.
%H A368376 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 A368376 G.f.: (x + x^2 * R(x) + R(x)^2) * R(x) / x^3, where R(x) = x * (A(x^2) - 1) and A(x) is the g.f. of A004148. - _Andrei Zabolotskii_, Jul 25 2025
%t A368376 r = (1 - z^4 - z^2 - Sqrt[z^8 - 2z^6 - z^4 - 2z^2 + 1]) / (2z^3);
%t A368376 gf = r (u^2 z + u z^2 + 1) / (z^3 (1 - r u));
%t A368376 Table[SeriesCoefficient[gf,{u,0,2},{z,0,n}], {n,0,33}] (* _Andrei Zabolotskii_, Jul 25 2025 *)
%Y A368376 Cf. A144366, A166297, A368377, A004148.
%Y A368376 A093128 is a bisection.
%K A368376 nonn
%O A368376 0,6
%A A368376 _N. J. A. Sloane_, Feb 18 2024
%E A368376 Terms a(14) and beyond from _Andrei Zabolotskii_, Jul 25 2025