cp's OEIS Frontend

A245123 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 4.

%I A245123 #9 Jul 12 2014 07:18:51
%S A245123 2,3,9,20,46,94,202,412,850,1719,3483,6987,14026,27990,55830,111022,
%T A245123 220589,437451,866898,1715821,3393973,6708016,13251455,26163174,
%U A245123 51635765,101868226,200908954,396129137,780868821,1538971204,3032575428,5974874666,11770477038
%N A245123 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 4.
%H A245123 Alois P. Heinz, <a href="/A245123/b245123.txt">Table of n, a(n) for n = 11..1000</a>
%e A245123 a(11) = 2:
%e A245123 :     o          o      :
%e A245123 :   /( )\     / ( ) \   :
%e A245123 :  o o o o   o  o o  o  :
%e A245123 :  | | |    ( ) | |     :
%e A245123 :  o o o    o o o o     :
%e A245123 :  | |      |   |       :
%e A245123 :  o o      o   o       :
%e A245123 :  |                    :
%e A245123 :  o                    :
%p A245123 b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
%p A245123       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
%p A245123        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
%p A245123     end:
%p A245123 A:= proc(n, k) option remember;
%p A245123       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
%p A245123     end:
%p A245123 a:= n-> b(n-1$2, 4$2):
%p A245123 seq(a(n), n=11..50);
%Y A245123 Column k=4 of A245120.
%K A245123 nonn
%O A245123 11,1
%A A245123 _Alois P. Heinz_, Jul 12 2014