A368380 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.

0, 0, 0, 1, 0, 5, 1, 20, 8, 75, 44, 275, 208, 1001, 910, 3640, 3808, 13260, 15504, 48450, 62016, 177650, 245157, 653752, 961400, 2414425, 3749460, 8947575, 14567280, 33266625, 56448210, 124062000, 218349120, 463991880, 843621600, 1739969550, 3257112960

Offset

0,6

Comments

It would be nice to have a more precise definition.

Links

Table of n, a(n) for n=0..36.

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 3.2.

Formula

G.f.: (1/x + 1 + 2*R(x) + R(x)^2) * R(x)^3 + R(x)^2 / x = F(x) * R(x), where R(x) = (1 - sqrt(1-4*x^2)) / (2*x^2) - 1 and F(x) is the g.f. of A368379. - Andrei Zabolotskii, Jul 25 2025

Crossrefs

Cf. A368378, A368379.

The two bisections are A115144 (shifted, negated) and A115147 (shifted, negated).

Sequence in context: A145372 A145373 A088577 * A127561 A144879 A049411

Adjacent sequences: A368377 A368378 A368379 * A368381 A368382 A368383

Keyword

nonn

Author

N. J. A. Sloane, Feb 18 2024

Extensions

Terms a(13) and beyond from Andrei Zabolotskii, Jul 25 2025

Status

approved