A263191 - OEIS

%I #26 Nov 15 2015 17:37:46

%S 1,1,1,1,1,2,1,0,1,1,3,2,2,2,0,2,0,1,0,0,0,0,1,1,4,3,5,4,2,4,0,5,2,0,

%T 2,0,3,0,1,0,0,2,0,0,0,2,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,5,4,

%U 9,6,7,6,3,10,6,4,4,0,9,5,2,0,4,4,4,0,0,4,3,1,0,2,4,0,4,0,0,0,3,0,0,2

%N Triangle read by rows: T(n>=0, 1<=k<=A000108(n)) is the number of Dyck paths of length 2n having k smaller elements in Tamari order.

%C Row sums give A000108.

%H Alois P. Heinz, <a href="/A263191/b263191.txt">Rows n = 0..10, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000032">The number of elements smaller than the given Dyck path in the Tamari Order</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tamari_lattice">Tamari lattice</a>.

%F Sum_{k=1..A000108(n)} k * T(n,k) = A000260(n). - _Alois P. Heinz_, Nov 15 2015

%e Triangle begins:

%e 1;

%e 1;

%e 1,1;

%e 1,2,1,0,1;

%e 1,3,2,2,2,0,2,0,1,0,0,0,0,1;

%e 1,4,3,5,4,2,4,0,5,2,0,2,0,3,0,1,0,0,2,0,0,0,2,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,1;

%e ...

%Y Cf. A000108, A000260.

%K nonn,tabf

%O 0,6

%A _Christian Stump_, Oct 19 2015

%E Two terms (for rows 0 and 1) prepended by _Alois P. Heinz_, Nov 15 2015