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A243829
Number A(n,k) of Dyck paths of semilength n having exactly three (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, 5, 0, 0, 0, 5, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 1, 20, 0, 0, 0, 0, 0, 0, 0, 10, 50, 0, 0, 0, 0, 0, 0, 1, 0, 50, 105, 0, 0, 0, 0, 0, 0, 0, 4, 5, 175, 196, 0, 0, 0, 0, 0, 0, 0, 0, 20, 56, 490, 336, 0, 0, 0, 0, 0, 0, 0, 1, 5, 80, 364, 1176, 540, 0, 0
OFFSET
0,10
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, ...
5, 5, 1, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 6, 1, 0, 1, 0, 0, 0, 0, ...
0, 0, 20, 10, 0, 4, 0, 1, 0, 0, ...
0, 0, 50, 50, 5, 20, 5, 6, 0, 0, ...
0, 0, 105, 175, 56, 80, 56, 35, 0, 5, ...
0, 0, 196, 490, 364, 315, 364, 168, 0, 49, ...
0, 0, 336, 1176, 1800, 1176, 1800, 750, 12, 280, ...
CROSSREFS
Main diagonal gives A243772 or column k=3 of A243752.
Sequence in context: A036297 A336530 A087935 * A329639 A318952 A089877
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved