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A243834
Number A(n,k) of Dyck paths of semilength n having exactly eight (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, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 1430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 4950, 0, 0
OFFSET
0,45
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, ...
1430, 1430, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 36, 1, 0, 1, 0, 0, 0, 0, 1, 0, ...
0, 0, 540, 45, 0, 9, 0, 1, 0, 0, 1, 0, ...
0, 0, 4950, 825, 0, 90, 0, 11, 0, 0, 19, 0, ...
CROSSREFS
Main diagonal gives A243777 or column k=8 of A243752.
Sequence in context: A353080 A238136 A060364 * A124087 A244105 A264181
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved