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A096588 a(n)=number of Catalan knight paths in Quadrant I from (0,0) to points on the vertical line x=n. A Catalan knight moves (2 right and 1 up) or (1 right and 1 down). 1

%I

%S 1,1,3,6,16,38,99,248,646,1659,4342,11307,29740,78115,206349,545156,

%T 1445332,3834559,10197168,27140709,72357778,193076677,515843630,

%U 1379308111,3691755414,9888374480,26507373732,71103941488,190859621124

%N a(n)=number of Catalan knight paths in Quadrant I from (0,0) to points on the vertical line x=n. A Catalan knight moves (2 right and 1 up) or (1 right and 1 down).

%H 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).

%F Row sums of array in A096587.

%e Rows of array T(n,k) in A096587:

%e 1

%e 0 0 1

%e 1 1 0 0 1

%e 0 1 2 2 0 0 1

%e ...

%e so a(3)=T(3,0)+T(3,1)+...+T(3,6)=6.

%Y Cf. A096587.

%K nonn,changed

%O 0,3

%A _Clark Kimberling_, Jun 28 2004

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Last modified July 4 20:08 EDT 2022. Contains 355086 sequences. (Running on oeis4.)