A368376 Arises from enumeration of a certain class of zig-zag knight's paths on the square grid.

0, 1, 0, 1, 0, 3, 1, 6, 3, 13, 9, 29, 25, 65, 66, 148, 171, 341, 437, 793, 1107, 1860, 2790, 4395, 7009, 10452, 17574, 24999, 44019, 60097, 110210, 145130, 275925, 351916, 690993, 856502, 1731224, 2091599, 4339980, 5123437, 10887192, 12585354, 27331465

Offset

0,6

Comments

It would be nice to have a more precise definition.

Links

Table of n, a(n) for n=0..42.

Jean-Luc Baril and José L. Ramírez, Knight's paths towards Catalan numbers, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087 [math.CO], Jan 2023. See Section 2.2.

Formula

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

Mathematica

r = (1 - z^4 - z^2 - Sqrt[z^8 - 2z^6 - z^4 - 2z^2 + 1]) / (2z^3);
gf = r (u^2 z + u z^2 + 1) / (z^3 (1 - r u));
Table[SeriesCoefficient[gf, {u, 0, 2}, {z, 0, n}], {n, 0, 33}] (* Andrei Zabolotskii, Jul 25 2025 *)

Crossrefs

Cf. A144366, A166297, A368377, A004148.

A093128 is a bisection.

Sequence in context: A294778 A132180 A207630 * A126191 A070883 A393195

Adjacent sequences: A368373 A368374 A368375 * A368377 A368378 A368379

Keyword

nonn

Author

N. J. A. Sloane, Feb 18 2024

Extensions

Terms a(14) and beyond from Andrei Zabolotskii, Jul 25 2025

Status

approved