A244709 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 8.

1, 1, 3, 6, 15, 31, 74, 159, 365, 803, 1813, 4022, 9038, 20128, 45093, 100656, 225263, 503320, 1126045, 2517487, 5631913, 12596046, 28181168, 63045684, 141071758, 315668674, 706452161, 1581088178, 3538954508, 7921759060, 17733983146, 39702719910, 88893039358

Offset

9,3

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 = 9..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, 8$2):
seq(a(n), n=9..50);

Crossrefs

Column k=8 of A244657.

Sequence in context: A319765 A244707 A244708 * A244710 A244711 A244712

Adjacent sequences: A244706 A244707 A244708 * A244710 A244711 A244712

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved