A318945 - OEIS

A318945

Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of Dyck paths with k valleys of altitude k.

1, 4, 1, 13, 5, 1, 39, 19, 6, 1, 112, 64, 26, 7, 1, 313, 201, 97, 34, 8, 1, 859, 603, 331, 139, 43, 9, 1, 2328, 1752, 1064, 512, 191, 53, 10, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

2,2

LINKS

Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., Enumerations of peaks and valleys on non-decreasing Dyck paths, Discrete Mathematics (2018), 341(10), 2789-2807.

EXAMPLE

Triangle begins:

4,1,

13,5,1,

39,19,6,1,

112,64,26,7,1,

313,201,97,34,8,1,

859,603,331,139,43,9,1,

2328,1752,1064,512,191,53,10,1,

...

CROSSREFS

Columns 0, 1, 2. 3 are A105693, A318946, A318947, A319405.

KEYWORD

nonn,tabl,more

AUTHOR

STATUS

approved