A122084 - OEIS

%I #4 Mar 30 2012 16:50:31

%S 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,

%T 36,88,98,45,10,1,1,8,49,155,249,181,64,11,1,1,9,64,250,535,576,308,

%U 85,13,1,1,10,81,377,1021,1506,1166,479,110,14,1,1,11,100,542,1786

%N 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.

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

%H R. W. Robinson, <a href="/A122084/b122084.txt">Rows 1 through 30, flattened</a>

%e 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.

%e 1 0 1

%e Total( 1) = 1

%e 1 1 1

%e Total( 2) = 1

%e 1 2 1

%e 2 1 1

%e Total( 3) = 2

%e 1 3 1

%e 2 2 2

%e 3 1 1

%e Total( 4) = 4

%e 1 4 1

%e 2 3 3

%e 3 2 4

%e 4 1 1

%e Total( 5) = 9

%e 1 5 1

%e 2 4 4

%e 3 3 9

%e 4 2 5

%e 5 1 1

%e Total( 6) = 20

%Y Row sums give A000081.

%K nonn,tabf

%O 1,6

%A _N. J. A. Sloane_, Oct 19 2006