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

Offset: 0

Author

Paul D. Hanna, Sep 19 2007, Oct 06 2007

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

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

Extensions

Extended by Martin Fuller, Sep 24 2007