A244707 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 6.

1, 1, 3, 6, 15, 31, 74, 157, 359, 786, 1766, 3895, 8710, 19287, 42987, 95437, 212468, 472204, 1050940, 2337221, 5201558, 11573156, 25759514, 57332239, 127633669, 284148877, 632704464, 1408925270, 3137861761, 6989057709, 15568767849, 34684141315, 77277619879

Offset

7,3

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 = 7..900

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, 6$2):
seq(a(n), n=7..50);

Crossrefs

Column k=6 of A244657.

Sequence in context: A293732 A117161 A319765 * A244708 A244709 A244710

Adjacent sequences: A244704 A244705 A244706 * A244708 A244709 A244710

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved