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.
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
Offset: 0
Examples
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]
Links
- Alois P. Heinz, Rows n = 0..270, flattened
Comments