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A245122 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 3.

%I A245122 #10 Jul 12 2014 05:48:15
%S A245122 1,2,4,9,17,35,67,131,249,484,922,1775,3393,6513,12461,23910,45806,
%T A245122 87903,168619,323796,621816,1195123,2297617,4420093,8506487,16380013,
%U A245122 31554394,60817066,117266799,226217218,436572777,842895506,1628036630,3145780899,6080759314
%N A245122 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 3.
%C A245122 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.
%H A245122 Alois P. Heinz, <a href="/A245122/b245122.txt">Table of n, a(n) for n = 7..1000</a>
%e A245122 a(8) = 2:
%e A245122 :    o        o     :
%e A245122 :   /|\     / | \   :
%e A245122 :  o o o   o  o  o  :
%e A245122 :  | |    ( ) |     :
%e A245122 :  o o    o o o     :
%e A245122 :  |      |         :
%e A245122 :  o      o         :
%e A245122 :  |                :
%e A245122 :  o                :
%p A245122 b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
%p A245122       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
%p A245122        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
%p A245122     end:
%p A245122 A:= proc(n, k) option remember;
%p A245122       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
%p A245122     end:
%p A245122 a:= n-> b(n-1$2, 3$2):
%p A245122 seq(a(n), n=7..45);
%Y A245122 Column k=3 of A245120.
%K A245122 nonn
%O A245122 7,2
%A A245122 _Alois P. Heinz_, Jul 12 2014