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A243752
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Number T(n,k) of Dyck paths of semilength n having exactly k (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1); triangle T(n,k), n>=0, read by rows.
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42
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1, 0, 1, 0, 1, 1, 1, 3, 1, 1, 11, 2, 9, 16, 12, 4, 1, 1, 57, 69, 5, 127, 161, 98, 35, 7, 1, 323, 927, 180, 1515, 1997, 1056, 280, 14, 4191, 5539, 3967, 1991, 781, 244, 64, 17, 1, 1, 10455, 25638, 18357, 4115, 220, 1, 20705, 68850, 77685, 34840, 5685, 246, 1
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OFFSET
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0,8
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LINKS
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EXAMPLE
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Triangle T(n,k) begins:
: n\k : 0 1 2 3 4 5 ...
+-----+----------------------------------------------------------
: 5 : 9, 16, 12, 4, 1; [row 5 of A091869]
: 6 : 1, 57, 69, 5; [row 6 of A091156]
: 7 : 127, 161, 98, 35, 7, 1; [row 7 of A092107]
: 8 : 323, 927, 180; [row 8 of A091958]
: 9 : 1515, 1997, 1056, 280, 14; [row 9 of A135306]
: 10 : 4191, 5539, 3967, 1991, 781, 244, ... [row 10 of A094507]
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CROSSREFS
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Columns k=0-10 give: A243754, A243770, A243771, A243772, A243773, A243774, A243775, A243776, A243777, A243778, A243779, or main diagonals of A243753, A243827, A243828, A243829, A243830, A243831, A243832, A243833, A243834, A243835, A243836.
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KEYWORD
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AUTHOR
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STATUS
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approved
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