editing

approved

In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.

b:= proc(n, i, h, v) option remember; `if`(n=0,

`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,

`if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)

*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))

end:

A:= proc(n, k) option remember;

`if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))

end:

a:= n-> b(n-1$2, 7$2):

seq(a(n), n=8..50);

Alois P. Heinz, <a href="/A244708/b244708.txt">Table of n, a(n) for n = 8..500</a>

allocated for Alois P. Heinz

Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 7.

1, 1, 3, 6, 15, 31, 74, 159, 363, 799, 1800, 3988, 8945, 19893, 44486, 99153, 221520, 494187, 1103789, 2463834, 5502927, 12288076, 27448039, 61308387, 136966368, 305999360, 683733350, 1527844853, 3414432569, 7631131801, 17056871547, 38127833992, 85235556468

8,3

Column k=7 of A244657.

allocated

nonn

Alois P. Heinz, Jul 04 2014

approved

editing

allocated for Alois P. Heinz

allocated

approved