A238094 - OEIS

A238094

Triangle read by rows: T(n,k) (n >= 1, k >= 0) = number of Dyck paths of semilength k avoiding the pattern U^n D^n.

%I #6 May 24 2018 13:21:30

%S 0,1,1,1,1,1,2,4,4,1,1,2,5,13,25,25,1,1,2,5,14,41,106,196,196,1,1,2,5,

%T 14,42,131,392,980,1764,1764,1,1,2,5,14,42,132,428,1380,4068,9864,

%U 17424,17424,1,1,2,5,14,42,132,429,1429,4797,15489,44649,105633,184041,184041,1,1,2,5,14,42,132,429,1430,4861,16714,56749,181258,511225

%N Triangle read by rows: T(n,k) (n >= 1, k >= 0) = number of Dyck paths of semilength k avoiding the pattern U^n D^n.

%C Row n has length 2n-1.

%H Axel Bacher, Antonio Bernini, Luca Ferrari, Benjamin Gunby, Renzo Pinzani, Julian West, <a href="http://dx.doi.org/10.1016/j.disc.2013.12.011">The Dyck pattern poset</a>, Discrete Math. 321 (2014), 12--23. MR3154009.

%e Triangle begins:

%e 0,

%e 1, 1, 1,

%e 1, 1, 2, 4, 4,

%e 1, 1, 2, 5, 13, 25, 25,

%e 1, 1, 2, 5, 14, 41, 106, 196, 196,

%e 1, 1, 2, 5, 14, 42, 131, 392, 980, 1764, 1764,

%e 1, 1, 2, 5, 14, 42, 132, 428, 1380, 4068, 9864, 17424, 17424,

%e 1, 1, 2, 5, 14, 42, 132, 429, 1429, 4797, 15489, 44649, 105633, 184041, 184041,

%e ...

%Y Rows converge to A000108. Right-hand edge is A001246.

%K nonn,tabf

%O 1,7

%A _N. J. A. Sloane_, Feb 21 2014