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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 A257894 A103997

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 October 15 14:07 EDT 2018. Contains 316236 sequences. (Running on oeis4.)