cp's OEIS Frontend

A132854 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 4th power of an integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with c(0)=1.

%I A132854 #11 Mar 14 2015 12:06:22
%S A132854 1,1,4,32,736,47600,9901728,6780161344,15819971230848,
%T A132854 128391245362464512,3685238521747987153664,
%U A132854 378871127417706380405937152,140962622184196263047081802452992,191428155805533938524028481989647915008
%N A132854 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 4th power of an integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with c(0)=1.
%C A132854 The minimal path in the 4-convoluted tree is A083954 and the maximal path is A132837.
%C A132854 Equals the number of nodes at generation n in the 4-convoluted tree, which is defined as follows: tree of all finite sequences {c(k), k=0..n} that form the initial terms of a self-convolution 4th power of some integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with a(0)=1. - _Paul D. Hanna_, Oct 06 2007
%H A132854 Martin Fuller, <a href="/A132852/a132852.txt">Computing A132852, A132853, A132854, A132855, A132856</a>
%e A132854 a(n) counts the nodes in generation n of the following tree.
%e A132854 Generations 0..3 of the 4-convoluted tree are as follows;
%e A132854 The path from the root is shown, with child nodes enclosed in [].
%e A132854 GEN.0: [1];
%e A132854 GEN.1: 1->[4];
%e A132854 GEN.2: 1-4->[2,6,10,14];
%e A132854 GEN.3:
%e A132854 1-4-2->[4,8]
%e A132854 1-4-6->[4,8,12,16,20,24]
%e A132854 1-4-10->[4,8,12,16,20,24,28,32,36,40]
%e A132854 1-4-14->[4,8,12,16,20,24,28,32,36,40,44,48,52,56].
%e A132854 Each path in the tree from the root node forms the initial terms of a self-convolution 4th power of a sequence of integer terms.
%Y A132854 Cf. A132852, A132853, A132855, A132856; A083954, A132837.
%K A132854 nonn
%O A132854 0,3
%A A132854 _Paul D. Hanna_, Sep 19 2007, Oct 06 2007
%E A132854 Extended by _Martin Fuller_, Sep 24 2007