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A243752 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. 42
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
EXAMPLE
Triangle T(n,k) begins:
: n\k : 0 1 2 3 4 5 ...
+-----+----------------------------------------------------------
: 0 : 1; [row 0 of A131427]
: 1 : 0, 1; [row 1 of A131427]
: 2 : 0, 1, 1; [row 2 of A090181]
: 3 : 1, 3, 1; [row 3 of A001263]
: 4 : 1, 11, 2; [row 4 of A091156]
: 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]
CROSSREFS
Row sums give A000108.
Sequence in context: A078688 A082466 A120270 * A113711 A339019 A257894
KEYWORD
nonn,tabf,look
AUTHOR
Alois P. Heinz, Jun 09 2014
STATUS
approved

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Last modified February 29 17:50 EST 2024. Contains 370428 sequences. (Running on oeis4.)