A244705 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.

1, 1, 3, 6, 15, 29, 68, 140, 312, 660, 1443, 3084, 6710, 14425, 31278, 67508, 146300, 316424, 685955, 1486008, 3223480, 6992012, 15179437, 32960891, 71617874, 155661971, 338508703, 736401503, 1602712182, 3489454243, 7600403101, 16560519877, 36097320801

Offset

5,3

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 = 5..1000

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, 4$2):
seq(a(n), n=5..50);

Crossrefs

Column k=4 of A244657.

Sequence in context: A034464 A116696 A000220 * A319643 A092641 A077449

Adjacent sequences: A244702 A244703 A244704 * A244706 A244707 A244708

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved