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A243832
Number A(n,k) of Dyck paths of semilength n having exactly six (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, 132, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 1176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 336, 5292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 2520, 19404, 0, 0
OFFSET
0,28
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, ...
132, 132, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 21, 1, 0, 1, 0, 0, 0, 0, 1, ...
0, 0, 196, 28, 0, 7, 0, 1, 0, 0, 1, ...
0, 0, 1176, 336, 0, 56, 0, 9, 0, 0, 15, ...
0, 0, 5292, 2520, 0, 336, 0, 80, 0, 0, 64, ...
CROSSREFS
Main diagonal gives A243775 or column k=6 of A243752.
Sequence in context: A267720 A263299 A330202 * A331909 A001295 A105684
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved