A243752 - OEIS

A243752

Number T(n,k) of Dyck paths of semilength n having exactly k (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1); triangle T(n,k), n>=0, read by rows.

1, 0, 1, 0, 1, 1, 1, 3, 1, 1, 11, 2, 9, 16, 12, 4, 1, 1, 57, 69, 5, 127, 161, 98, 35, 7, 1, 323, 927, 180, 1515, 1997, 1056, 280, 14, 4191, 5539, 3967, 1991, 781, 244, 64, 17, 1, 1, 10455, 25638, 18357, 4115, 220, 1, 20705, 68850, 77685, 34840, 5685, 246, 1

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OFFSET

0,8

LINKS

Alois P. Heinz, Rows n = 0..270, flattened

EXAMPLE

Triangle T(n,k) begins:

: n\k : 0 1 2 3 4 5 ...

+-----+----------------------------------------------------------

: 0 : 1; [row 0 of A131427]

: 1 : 0, 1; [row 1 of A131427]

: 2 : 0, 1, 1; [row 2 of A090181]