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A243829
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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.
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13
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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
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OFFSET
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0,10
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LINKS
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EXAMPLE
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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, ...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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