%I A122085
%S A122085 1,1,1,1,1,1,1,1,1,2,2,1,1,2,4,2,1,1,3,7,7,3,1,1,3,10,14,10,3,1,1,4,
%T A122085 14,28,28,14,4,1,1,4,19,45,65,45,19,4,1,1,5,24,73,132,132,73,24,5,1,
%U A122085 1,5,30,105,242,316,242,105,30,5,1,1,6,37,152,412,693,693,412,152
%N A122085 Triangle read by rows: T(n,k) = number of unlabeled free bicolored trees 
               with n nodes (n >= 1) and k (1 <= k <= n-1, except k=0 or 1 if n=1, 
               k=1 if n=2) nodes of one color and n-k nodes of the other color (the 
               colors are not interchangeable).
%D A122085 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H A122085 R. W. Robinson, <a href="b122085.txt">Rows 1 through 30, flattened</a>
%e A122085 K M N gives the number N of unlabeled free bicolored trees with K nodes 
               of one color and M nodes of the other color.
%e A122085 0 1 1
%e A122085 1 0 1
%e A122085 Total( 1) = 2
%e A122085 1 1 1
%e A122085 Total( 2) = 1
%e A122085 1 2 1
%e A122085 2 1 1
%e A122085 Total( 3) = 2
%e A122085 1 3 1
%e A122085 2 2 1
%e A122085 3 1 1
%e A122085 Total( 4) = 3
%e A122085 1 4 1
%e A122085 2 3 2
%e A122085 3 2 2
%e A122085 4 1 1
%e A122085 Total( 5) = 6
%e A122085 1 5 1
%e A122085 2 4 2
%e A122085 3 3 4
%e A122085 4 2 2
%e A122085 5 1 1
%e A122085 Total( 6) = 10
%Y A122085 Row sums give A122086.
%Y A122085 Sequence in context: A075402 A088855 A034851 this_sequence A066287 A059260 
               A135229
%Y A122085 Adjacent sequences: A122082 A122083 A122084 this_sequence A122086 A122087 
               A122088
%K A122085 nonn,tabf
%O A122085 1,10
%A A122085 N. J. A. Sloane (njas(AT)research.att.com), Oct 19 2006