0,3

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 6-th power of some integer sequence such that 0 < c(n) <= 6*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 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 6-th power of a sequence of integer terms.

Cf. A132852, A132853, A132854, A132855; A083956.

Sequence in context: A122722 A127946 A012503 this_sequence A041149 A119814 A050884

Adjacent sequences: A132853 A132854 A132855 this_sequence A132857 A132858 A132859

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.