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 A368379 #15 Jul 26 2025 14:39:12
%S A368379 0,1,0,3,1,9,6,28,27,90,110,297,429,1001,1638,3432,6188,11934,23256,
%T A368379 41990,87210,149226,326876,534888,1225785,1931540,4601610,7020405,
%U A368379 17298645,25662825,65132550,94287120,245642760,347993910,927983760,1289624490,3511574910
%N A368379 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.
%C A368379 It would be nice to have a more precise definition.
%H A368379 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 A368379 G.f.: (1/x + 1 + 2*R(x) + R(x)^2) * R(x)^2 + R(x) / x = (F(x) + 1/x) * R(x), where R(x) = (1 - sqrt(1-4*x^2)) / (2*x^2) - 1 and F(x) is the g.f. of A368378. - _Andrei Zabolotskii_, Jul 25 2025
%t A368379 r = (1 - 2z^2 - Sqrt[1-4z^2]) / (2z^2);
%t A368379 gf = (r^2 z + r u^2 + r u + 2 r z + z) / (z (1 - r u));
%t A368379 Table[SeriesCoefficient[gf,{u,0,2},{z,0,n}], {n,0,50}] (* _Andrei Zabolotskii_, Jul 25 2025 *)
%Y A368379 Cf. A368378, A368380.
%Y A368379 The two bisections are A000245 and A115145 (shifted, negated).
%K A368379 nonn
%O A368379 0,4
%A A368379 _N. J. A. Sloane_, Feb 18 2024
%E A368379 Terms a(11) and beyond from _Andrei Zabolotskii_, Jul 25 2025