OFFSET

0,3

COMMENTS

The minimal path in the 5-convoluted tree is A083956.

Equals the number of nodes at generation n in the 6-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 6th power of some integer sequence such that 0 < c(n) <= 6*c(n-1) for n>0 with a(0)=1.

LINKS

EXAMPLE

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

Generations 0..3 of the 6-convoluted tree are as follows;

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

GEN.0: [1];

GEN.1: 1->[6];

GEN.2: 1-6->[3,9,15,21,27,33];

GEN.3:

1-6-3->[2,8,14]

1-6-9->[2,8,14,20,26,32,38,44,50]

1-6-15->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86]

1-6-21->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122]

1-6-27->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,128,134,140,146,152,158]

1-6-33->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,128,134,140,146,152,158,164,170,176,182,188,194].

Each path in the tree from the root node forms the initial terms of a self-convolution 6th power of a sequence of integer terms.

CROSSREFS

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Extended by Martin Fuller, Sep 24 2007

STATUS

approved