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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 Alois P. Heinz, Rows n = 0..270, flattened 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 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. Row sums give A000108. Cf. A098978, A114463, A114848, A116424, A135305, A242450, A243366, A243838. Sequence in context: A078688 A082466 A120270 * A113711 A339019 A257894 Adjacent sequences: A243749 A243750 A243751 * A243753 A243754 A243755 KEYWORD nonn,tabf,look AUTHOR Alois P. Heinz, Jun 09 2014 STATUS approved

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Last modified September 29 00:22 EDT 2023. Contains 365739 sequences. (Running on oeis4.)