OFFSET
0,4
COMMENTS
It would be nice to have a more precise definition.
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.
FORMULA
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
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, 2}, {z, 0, n}], {n, 0, 50}] (* Andrei Zabolotskii, Jul 25 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 18 2024
EXTENSIONS
Terms a(11) and beyond from Andrei Zabolotskii, Jul 25 2025
STATUS
approved
