cp's OEIS Frontend

A132855 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 5th power of an integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with c(0)=1.

%I A132855 #8 Mar 13 2015 22:44:52
%S A132855 1,1,5,75,3625,638750,442823125,1278820631250,15775429658296875,
%T A132855 848938273203627578125,202483260558673741179296875,
%U A132855 216741216953142470752123517187500,1051774892873652266440974611041742187500
%N A132855 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 5th power of an integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with c(0)=1.
%C A132855 The minimal path in the 5-convoluted tree is A083955 and the maximal path is A132839.
%C A132855 Equals the number of nodes at generation n in the 5-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 5th power of some integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with a(0)=1.
%H A132855 Martin Fuller, <a href="/A132852/a132852.txt">Computing A132852, A132853, A132854, A132855, A132856</a>
%e A132855 a(n) counts the nodes in generation n of the following tree.
%e A132855 Generations 0..3 of the 5-convoluted tree are as follows;
%e A132855 The path from the root is shown, with child nodes enclosed in [].
%e A132855 GEN.0: [1];
%e A132855 GEN.1: 1->[5];
%e A132855 GEN.2: 1-5->[5,10,15,20,25];
%e A132855 GEN.3:
%e A132855 1-5-5->[5,10,15,20,25]
%e A132855 1-5-10->[5,10,15,20,25,30,35,40,45,50]
%e A132855 1-5-15->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75]
%e A132855 1-5-20->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100]
%e A132855 1-5-25->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105, 110,115,120,125].
%e A132855 Each path in the tree from the root node forms the initial terms of a self-convolution 5th power of a sequence of integer terms.
%Y A132855 Cf. A132852, A132853, A132854, A132856; A083955, A132839.
%K A132855 nonn
%O A132855 0,3
%A A132855 _Paul D. Hanna_, Sep 19 2007, Oct 06 2007
%E A132855 Extended by _Martin Fuller_, Sep 24 2007