A243830 - OEIS

A243830

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

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 50, 0, 0, 0, 0, 0, 0, 0, 0, 15, 175, 0, 0, 0, 0, 0, 0, 0, 1, 0, 105, 490, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 490, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 14, 1764, 2520, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 140, 210, 5292, 4950, 0, 0

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OFFSET

0,15

LINKS

Alois P. Heinz, Antidiagonals n = 0..140, flattened

EXAMPLE

Square array A(n,k) begins:

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

14, 14, 1, 0, 0, 0, 0, 0, 0, 0, ...

0, 0, 10, 1, 0, 1, 0, 0, 0, 0, ...

0, 0, 50, 15, 0, 5, 0, 1, 0, 0, ...

0, 0, 175, 105, 0, 30, 0, 7, 0, 0, ...