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 A368380 #19 Jul 26 2025 10:03:36 %S A368380 0,0,0,1,0,5,1,20,8,75,44,275,208,1001,910,3640,3808,13260,15504, %T A368380 48450,62016,177650,245157,653752,961400,2414425,3749460,8947575, %U A368380 14567280,33266625,56448210,124062000,218349120,463991880,843621600,1739969550,3257112960 %N A368380 Arises from enumeration of a certain class of partial zig-zag knight's paths on the square grid. %C A368380 It would be nice to have a more precise definition. %H A368380 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 A368380 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 %Y A368380 Cf. A368378, A368379. %Y A368380 The two bisections are A115144 (shifted, negated) and A115147 (shifted, negated). %K A368380 nonn %O A368380 0,6 %A A368380 _N. J. A. Sloane_, Feb 18 2024 %E A368380 Terms a(13) and beyond from _Andrei Zabolotskii_, Jul 25 2025