A122084 Triangle read by rows: T(n,k) = number of unlabeled rooted bicolored trees with n nodes (n >= 1) in which k (1 <= k <= n-1, except k=1 if n=1) nodes have even distance from the root and n-k nodes have odd distance from the root.

1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 5, 1, 1, 5, 16, 18, 7, 1, 1, 6, 25, 44, 30, 8, 1, 1, 7, 36, 88, 98, 45, 10, 1, 1, 8, 49, 155, 249, 181, 64, 11, 1, 1, 9, 64, 250, 535, 576, 308, 85, 13, 1, 1, 10, 81, 377, 1021, 1506, 1166, 479, 110, 14, 1, 1, 11, 100, 542, 1786

Offset

1,6

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 rooted bicolored trees in which K nodes have even distance from the root and M nodes have odd distance from the root.
1 0 1
Total( 1) = 1
1 1 1
Total( 2) = 1
1 2 1
2 1 1
Total( 3) = 2
1 3 1
2 2 2
3 1 1
Total( 4) = 4
1 4 1
2 3 3
3 2 4
4 1 1
Total( 5) = 9
1 5 1
2 4 4
3 3 9
4 2 5
5 1 1
Total( 6) = 20

Crossrefs

Row sums give A000081.

Sequence in context: A096465 A124460 A144042 * A104559 A080853 A071922

Adjacent sequences: A122081 A122082 A122083 * A122085 A122086 A122087

Keyword

nonn,tabf

Author

N. J. A. Sloane, Oct 19 2006

Status

approved