A244708 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

Offset

8,3

Comments

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 8..500

Maple

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);

Crossrefs

Column k=7 of A244657.

Sequence in context: A117161 A319765 A244707 * A244709 A244710 A244711

Adjacent sequences: A244705 A244706 A244707 * A244709 A244710 A244711

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved