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A122087
Triangle read by rows: T(n,k) = number of unlabeled free bicolored trees with n nodes (n >= 1) and k (1 <= k <= floor(n/2), except k = 0 if n = 1 ) nodes of one color and n-k nodes of the other color (the colors are interchangeable).
1
1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 3, 7, 1, 3, 10, 9, 1, 4, 14, 28, 1, 4, 19, 45, 37, 1, 5, 24, 73, 132, 1, 5, 30, 105, 242, 168, 1, 6, 37, 152, 412, 693, 1, 6, 44, 204, 660, 1349, 895, 1, 7, 52, 274, 1008, 2472, 3927, 1, 7, 61, 351, 1479, 4219, 8105, 5097, 1, 8
OFFSET
1,7
REFERENCES
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
LINKS
FORMULA
T(n,k) = A329054(k, n-k) for 2*k < n; T(2*n,n) = A119856(n). - Andrew Howroyd, Apr 04 2023
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
Total( 1) = 1
1 1 1
Total( 2) = 1
1 2 1
Total( 3) = 1
1 3 1
2 2 1
Total( 4) = 2
1 4 1
2 3 2
Total( 5) = 3
1 5 1
2 4 2
3 3 3
Total( 6) = 6
1 6 1
2 5 3
3 4 7
Total( 7) = 11
1 7 1
2 6 3
3 5 10
4 4 9
Total( 8) = 23
From Andrew Howroyd, Apr 05 2023: (Start)
Triangle begins:
n\k| 0 1 2 3 4 5 6
----+----------------------------
1 | 1;
2 | . 1;
3 | . 1;
4 | . 1, 1;
5 | . 1, 2;
6 | . 1, 2, 3;
7 | . 1, 3, 7;
8 | . 1, 3, 10, 9;
9 | . 1, 4, 14, 28;
10 | . 1, 4, 19, 45, 37;
11 | . 1, 5, 24, 73, 132;
12 | . 1, 5, 30, 105, 242, 168;
...
(End)
CROSSREFS
Row sums give A000055.
Cf. A119856, A329054, A362019 (labeled version).
Sequence in context: A144215 A254539 A283827 * A139642 A264744 A354322
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Oct 19 2006
STATUS
approved