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A243833
Number A(n,k) of Dyck paths of semilength n having exactly seven (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.
13
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 429, 0, 0, 0, 0, 0, 0, 0, 429, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 2520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 540, 13860, 0, 0
OFFSET
0,36
LINKS
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
429, 429, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 28, 1, 0, 1, 0, 0, 0, 0, 1, ...
0, 0, 336, 36, 0, 8, 0, 1, 0, 0, 1, ...
0, 0, 2520, 540, 0, 72, 0, 10, 0, 0, 17, ...
CROSSREFS
Main diagonal gives A243776 or column k=7 of A243752.
Sequence in context: A233812 A231047 A177328 * A334558 A320712 A338344
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved