0,3

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 5-th power of some integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with a(0)=1.

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 5-th power of a sequence of integer terms.

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

Sequence in context: A030986 A091882 A034688 this_sequence A051481 A011918 A136300

Adjacent sequences: A132852 A132853 A132854 this_sequence A132856 A132857 A132858

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Sep 19 2007, Oct 06 2007

Extended by Martin Fuller (martin_n_fuller(AT)btinternet.com), Sep 24 2007.