cp's OEIS Frontend

A246565 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly increasing.

%I A246565 #10 Aug 31 2014 02:00:41
%S A246565 1,1,2,3,6,9,20,31,67,115,238,406,880,1494,3118,5568,11408,20092,
%T A246565 41938,73687,151529,272359,552611,987277,2033173,3617167,7371745,
%U A246565 13318869,26991289,48496985,99264686,177917588,362349258,655925568,1331038563,2401097768,4913906801,8844673793,18046697901,32720071992,66666578597
%N A246565 Number of rooted ordered trees with n non-root nodes such that the branch lengths are weakly increasing.
%H A246565 Joerg Arndt, <a href="/A246565/a246565.txt">All trees for 0 <= n <= 7</a>
%e A246565 The a(4) = 6 such trees are:
%e A246565 :
%e A246565 :   1:
%e A246565 :  [ 1 1 1 1 ]
%e A246565 :  [ 0 0 0 0 ]
%e A246565 :
%e A246565 :  O--o
%e A246565 :  .--o
%e A246565 :  .--o
%e A246565 :  .--o
%e A246565 :
%e A246565 :
%e A246565 :   2:
%e A246565 :  [ 1 1 2 ]
%e A246565 :  [ 0 0 0 ]
%e A246565 :
%e A246565 :  O--o
%e A246565 :  .--o
%e A246565 :  .--o--o
%e A246565 :
%e A246565 :
%e A246565 :   3:
%e A246565 :  [ 1 3 ]
%e A246565 :  [ 0 0 ]
%e A246565 :
%e A246565 :  O--o
%e A246565 :  .--o--o--o
%e A246565 :
%e A246565 :
%e A246565 :   4:
%e A246565 :  [ 2 2 ]
%e A246565 :  [ 0 0 ]
%e A246565 :
%e A246565 :  O--o--o
%e A246565 :  .--o--o
%e A246565 :
%e A246565 :
%e A246565 :   5:
%e A246565 :  [ 2 2 ]
%e A246565 :  [ 0 1 ]
%e A246565 :
%e A246565 :  O--o--o
%e A246565 :     .--o--o
%e A246565 :
%e A246565 :
%e A246565 :   6:
%e A246565 :  [ 4 ]
%e A246565 :  [ 0 ]
%e A246565 :
%e A246565 :  O--o--o--o--o
%e A246565 :
%e A246565 See the Arndt link for all trees for 0 <= n <= 7.
%Y A246565 Cf. A000108 (all trees), A246566 (descending branch lengths), A193196, A192243.
%K A246565 nonn
%O A246565 0,3
%A A246565 _Joerg Arndt_, Aug 30 2014