A292230 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals four.

1, 2, 7, 22, 72, 230, 751, 2442, 8006, 26280, 86604, 285994, 946866, 3140812, 10438300, 34747649, 115849084, 386779317, 1292998720, 4327654320, 14500841169, 48639319376, 163308287353, 548820437392, 1845999502151, 6214297279692, 20935992503127, 70586182742450

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Index entries for sequences related to rooted trees

Example

: a(6) = 7:
:           o             o            o             o
:          / \          /   \        /( )\         / | \
:         o   N        o     N      o N N N       o  N  N
:        / \         /( )\         / \          /( )\
:       o   N       o N N N       o   N        N N N N
:     /( )\        ( )           ( )
:    N N N N       N N           N N
:
:          o            o              o
:        /   \        /( )\         / ( \ \
:       o     o      o N N N      o   o  N N
:     /( )\  ( )    /|\          ( ) ( )
:    N N N N N N   N N N         N N N N
:

Maple

b:= proc(n, i, v, k) option remember; `if`(n=0,
      `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
      `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
       b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
    end:
A:= proc(n, k) option remember; `if`(n<2, n,
      add(b(n, n+1-j, j, k), j=2..min(n, k)))
    end:
a:= n-> A(n, 4)-A(n, 3):
seq(a(n), n=4..35);

Crossrefs

Column k=4 of A292086.

Sequence in context: A092690 A030186 A289592 * A162770 A116387 A337805

Adjacent sequences: A292227 A292228 A292229 * A292231 A292232 A292233

Keyword

nonn

Author

Alois P. Heinz, Sep 12 2017

Status

approved