A132855 - OEIS

%I #8 Mar 13 2015 22:44:52

%S 1,1,5,75,3625,638750,442823125,1278820631250,15775429658296875,

%T 848938273203627578125,202483260558673741179296875,

%U 216741216953142470752123517187500,1051774892873652266440974611041742187500

%N 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 The minimal path in the 5-convoluted tree is A083955 and the maximal path is A132839.

%C 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 Martin Fuller, <a href="/A132852/a132852.txt">Computing A132852, A132853, A132854, A132855, A132856</a>

%e a(n) counts the nodes in generation n of the following tree.

%e Generations 0..3 of the 5-convoluted tree are as follows;

%e The path from the root is shown, with child nodes enclosed in [].

%e GEN.0: [1];

%e GEN.1: 1->[5];

%e GEN.2: 1-5->[5,10,15,20,25];

%e GEN.3:

%e 1-5-5->[5,10,15,20,25]

%e 1-5-10->[5,10,15,20,25,30,35,40,45,50]

%e 1-5-15->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75]

%e 1-5-20->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100]

%e 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 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 Cf. A132852, A132853, A132854, A132856; A083955, A132839.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 19 2007, Oct 06 2007

%E Extended by _Martin Fuller_, Sep 24 2007