A368378 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid.
0, 1, 1, 2, 4, 5, 14, 14, 48, 42, 165, 132, 572, 429, 2002, 1430, 7072, 4862, 25194, 16796, 90440, 58786, 326876, 208012, 1188640, 742900, 4345965, 2674440, 15967980, 9694845, 58929450, 35357670, 218349120, 129644790, 811985790, 477638700, 3029594040
Offset: 0
Keywords
Links
- 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.
Crossrefs
Programs
-
Mathematica
r = (1 - 2z^2 - Sqrt[1-4z^2]) / (2z^2); gf = (r^2 z + r u^2 + r u + 2 r z + z) / (z (1 - r u)); Table[SeriesCoefficient[gf,{u,0,1},{z,0,n}], {n,0,50}] (* Andrei Zabolotskii, Jul 25 2025 *)
Formula
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
Extensions
Terms a(11) and beyond from Andrei Zabolotskii, Jul 25 2025
Comments