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A243835
Number A(n,k) of Dyck paths of semilength n having exactly nine (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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 825, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 9075, 0, 0
OFFSET
0,55
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, 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, ...
4862, 4862, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 45, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...
0, 0, 825, 55, 0, 10, 0, 1, 0, 0, 1, 0, ...
CROSSREFS
Main diagonal gives A243778 or column k=9 of A243752.
Sequence in context: A031838 A331664 A031826 * A124088 A244106 A264182
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved