A292229 - OEIS

%I #10 Sep 12 2017 11:53:42

%S 1,2,6,17,47,133,380,1096,3186,9351,27618,82168,245882,740003,2238186,

%T 6801375,20754977,63583715,195486605,603003882,1865692570,5788676649,

%U 18007192835,56151236196,175486946089,549586009252,1724530420457,5421195811358,17070958403725

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

%H Alois P. Heinz, <a href="/A292229/b292229.txt">Table of n, a(n) for n = 3..1000</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%e : a(5) = 6:

%e :        o        o        o        o          o         o

%e :       / \      / \      /|\     /   \       /|\      / | \

%e :      o   N    o   N    o N N   o     o     o N N   o   o  N

%e :     / \      /|\      / \     /|\   ( )   /|\     ( ) ( )

%e :    o   N    o N N    o   N   N N N  N N  N N N    N N N N

%e :   /|\      ( )      ( )

%e :  N N N     N N      N N

%e :

%p b:= proc(n, i, v, k) option remember; `if`(n=0,

%p       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,

%p       `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*

%p        b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))

%p     end:

%p A:= proc(n, k) option remember; `if`(n<2, n,

%p       add(b(n, n+1-j, j, k), j=2..min(n, k)))

%p     end:

%p a:= n-> A(n, 3)-A(n, 2):

%p seq(a(n), n=3..35);

%Y Column k=3 of A292086.

%K nonn

%O 3,2

%A _Alois P. Heinz_, Sep 12 2017