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A243828
Number A(n,k) of Dyck paths of semilength n having exactly two (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.
14
0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 6, 10, 0, 0, 0, 0, 0, 1, 2, 20, 15, 0, 0, 0, 0, 0, 0, 3, 15, 50, 21, 0, 0, 0, 0, 0, 0, 2, 12, 69, 105, 28, 0, 0, 0, 0, 0, 0, 1, 15, 40, 252, 196, 36, 0, 0, 0, 0, 0, 0, 0, 5, 69, 135, 804, 336, 45, 0, 0
OFFSET
0,6
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, ...
2, 2, 1, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 3, 1, 0, 1, 0, 0, 0, 0, ...
0, 0, 6, 6, 2, 3, 2, 1, 0, 0, ...
0, 0, 10, 20, 15, 12, 15, 5, 0, 2, ...
0, 0, 15, 50, 69, 40, 69, 24, 3, 15, ...
0, 0, 21, 105, 252, 135, 252, 98, 28, 69, ...
0, 0, 28, 196, 804, 441, 804, 378, 180, 273, ...
0, 0, 36, 336, 2349, 1428, 2349, 1386, 954, 1056, ...
CROSSREFS
Main diagonal gives A243771 or column k=2 of A243752.
Sequence in context: A000095 A258322 A258034 * A034949 A263767 A185338
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved