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A243831
Number A(n,k) of Dyck paths of semilength n having exactly five (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, 42, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 1, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 490, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 196, 1764, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1176, 5292, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 5292, 13860, 0, 0
OFFSET
0,21
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, ...
42, 42, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 15, 1, 0, 1, 0, 0, 0, 0, 1, ...
0, 0, 105, 21, 0, 6, 0, 1, 0, 0, 1, ...
0, 0, 490, 196, 0, 42, 0, 8, 0, 0, 13, ...
0, 0, 1764, 1176, 0, 224, 0, 63, 0, 0, 52, ...
0, 0, 5292, 5292, 42, 1134, 42, 390, 0, 0, 244, ...
CROSSREFS
Main diagonal gives A243774 or column k=5 of A243752.
Sequence in context: A237639 A095189 A023932 * A022074 A335188 A263303
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jun 11 2014
STATUS
approved