cp's OEIS Frontend

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

%I A292230 #7 Sep 12 2017 11:54:04
%S A292230 1,2,7,22,72,230,751,2442,8006,26280,86604,285994,946866,3140812,
%T A292230 10438300,34747649,115849084,386779317,1292998720,4327654320,
%U A292230 14500841169,48639319376,163308287353,548820437392,1845999502151,6214297279692,20935992503127,70586182742450
%N A292230 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals four.
%H A292230 Alois P. Heinz, <a href="/A292230/b292230.txt">Table of n, a(n) for n = 4..1000</a>
%H A292230 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%e A292230 : a(6) = 7:
%e A292230 :           o             o            o             o
%e A292230 :          / \          /   \        /( )\         / | \
%e A292230 :         o   N        o     N      o N N N       o  N  N
%e A292230 :        / \         /( )\         / \          /( )\
%e A292230 :       o   N       o N N N       o   N        N N N N
%e A292230 :     /( )\        ( )           ( )
%e A292230 :    N N N N       N N           N N
%e A292230 :
%e A292230 :          o            o              o
%e A292230 :        /   \        /( )\         / ( \ \
%e A292230 :       o     o      o N N N      o   o  N N
%e A292230 :     /( )\  ( )    /|\          ( ) ( )
%e A292230 :    N N N N N N   N N N         N N N N
%e A292230 :
%p A292230 b:= proc(n, i, v, k) option remember; `if`(n=0,
%p A292230       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A292230       `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
%p A292230        b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p A292230     end:
%p A292230 A:= proc(n, k) option remember; `if`(n<2, n,
%p A292230       add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p A292230     end:
%p A292230 a:= n-> A(n, 4)-A(n, 3):
%p A292230 seq(a(n), n=4..35);
%Y A292230 Column k=4 of A292086.
%K A292230 nonn
%O A292230 4,2
%A A292230 _Alois P. Heinz_, Sep 12 2017