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.

1, 1, 4, 32, 736, 47600, 9901728, 6780161344, 15819971230848, 128391245362464512, 3685238521747987153664, 378871127417706380405937152, 140962622184196263047081802452992, 191428155805533938524028481989647915008

Offset: 0

Author

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

Keywords

• nonn

Comments

The minimal path in the 4-convoluted tree is A083954 and the maximal path is A132837.

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

Examples

			a(n) counts the nodes in generation n of the following tree.
Generations 0..3 of the 4-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[4];
GEN.2: 1-4->[2,6,10,14];
GEN.3:
1-4-2->[4,8]
1-4-6->[4,8,12,16,20,24]
1-4-10->[4,8,12,16,20,24,28,32,36,40]
1-4-14->[4,8,12,16,20,24,28,32,36,40,44,48,52,56].
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.
		

Links

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

Crossrefs

Cf. A132852, A132853, A132855, A132856; A083954, A132837.

Extensions

Extended by Martin Fuller, Sep 24 2007