

A122085


Triangle read by rows: T(n,k) = number of unlabeled free bicolored trees with n nodes (n >= 1) and k (1 <= k <= n1, except k=0 or 1 if n=1, k=1 if n=2) nodes of one color and nk nodes of the other color (the colors are not interchangeable).


2



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, 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, 1, 5, 30, 105, 242, 316, 242, 105, 30, 5, 1, 1, 6, 37, 152, 412, 693, 693, 412, 152
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,10


REFERENCES

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.


LINKS

R. W. Robinson, Rows 1 through 30, flattened


EXAMPLE

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.
0 1 1
1 0 1
Total( 1) = 2
1 1 1
Total( 2) = 1
1 2 1
2 1 1
Total( 3) = 2
1 3 1
2 2 1
3 1 1
Total( 4) = 3
1 4 1
2 3 2
3 2 2
4 1 1
Total( 5) = 6
1 5 1
2 4 2
3 3 4
4 2 2
5 1 1
Total( 6) = 10


CROSSREFS

Row sums give A122086.
Sequence in context: A034851 A172453 A172479 * A209612 A209805 A238453
Adjacent sequences: A122082 A122083 A122084 * A122086 A122087 A122088


KEYWORD

nonn,tabf


AUTHOR

N. J. A. Sloane, Oct 19 2006


STATUS

approved



