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 A368378 #14 Jul 26 2025 14:39:16
%S A368378 0,1,1,2,4,5,14,14,48,42,165,132,572,429,2002,1430,7072,4862,25194,
%T A368378 16796,90440,58786,326876,208012,1188640,742900,4345965,2674440,
%U A368378 15967980,9694845,58929450,35357670,218349120,129644790,811985790,477638700,3029594040
%N A368378 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.
%C A368378 It would be nice to have a more precise definition.
%H A368378 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 3.2.
%F A368378 G.f.: (1/x + 1 + 2*R(x) + R(x)^2) * R(x), where R(x) = (1 - sqrt(1-4*x^2)) / (2*x^2) - 1. - _Andrei Zabolotskii_, Jul 25 2025
%t A368378 r = (1 - 2z^2 - Sqrt[1-4z^2]) / (2z^2);
%t A368378 gf = (r^2 z + r u^2 + r u + 2 r z + z) / (z (1 - r u));
%t A368378 Table[SeriesCoefficient[gf,{u,0,1},{z,0,n}], {n,0,50}] (* _Andrei Zabolotskii_, Jul 25 2025 *)
%Y A368378 Cf. A368379, A368380.
%Y A368378 The two bisections are A000108 and A099376. The first differences are A026008.
%K A368378 nonn
%O A368378 0,4
%A A368378 _N. J. A. Sloane_, Feb 18 2024
%E A368378 Terms a(11) and beyond from _Andrei Zabolotskii_, Jul 25 2025