A246566 - OEIS

%I #7 Aug 31 2014 02:00:36

%S 1,1,2,4,10,24,62,155,396,992,2504,6228,15512,38220,94059,229498,

%T 558642,1350384,3255138,7801327,18642118,44329833,105111283,248184255,

%U 584396849,1371048495,3208318247,7483522231,17413665881,40405120865,93543352492

%N Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly decreasing.

%H Joerg Arndt, <a href="/A246566/a246566.txt">All trees for 0 <= n <= 5</a>

%e The a(3) = 4 such trees are:

%e :

%e :     1:

%e :    [ 1 1 1 ]

%e :    [ 0 0 0 ]

%e :

%e :  O--o

%e :  .--o

%e :  .--o

%e :

%e :

%e :     2:

%e :    [ 2 1 ]

%e :    [ 0 0 ]

%e :

%e :  O--o--o

%e :  .--o

%e :

%e :

%e :     3:

%e :    [ 2 1 ]

%e :    [ 0 1 ]

%e :

%e :  O--o--o

%e :     .--o

%e :

%e :

%e :     4:

%e :    [ 3 ]

%e :    [ 0 ]

%e :

%e :  O--o--o--o

%e :

%e See the Arndt link for all trees for 0 <= n <= 5.

%Y Cf. A000108 (all trees), A246565 (ascending branch lengths), A193196, A192243, A001519.

%K nonn

%O 0,3

%A _Joerg Arndt_, Aug 30 2014