A132855 - OEIS

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.

1, 1, 5, 75, 3625, 638750, 442823125, 1278820631250, 15775429658296875, 848938273203627578125, 202483260558673741179296875, 216741216953142470752123517187500, 1051774892873652266440974611041742187500

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OFFSET

0,3

COMMENTS

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

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.

LINKS

Table of n, a(n) for n=0..12.

Martin Fuller, Computing A132852, A132853, A132854, A132855, A132856

EXAMPLE

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

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

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

GEN.0: [1];

GEN.1: 1->[5];

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

GEN.3:

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