0,3

Equals the number of nodes at generation n in the 3-convoluted tree. The minimal path in the 3-convoluted tree is A083953 and the maximal path is A132835. The 3-convoluted tree is defined as follows: tree of all finite sequences {c(k), k=0..n} that form the initial terms of a self-convolution cube of some integer sequence such that 0 < c(n) <= 3*c(n-1) for n>0 with a(0)=1.

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

Generations 0..4 of the 3-convoluted tree are as follows;

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

GEN.0: [1];

GEN.1: 1->[3];

GEN.2: 1-3->[3,6,9];

GEN.3:

1-3-3->[1,4,7]

1-3-6->[1,4,7,10,13,16]

1-3-9->[1,4,7,10,13,16,19,22,25];

GEN.4:

1-3-3-1->[3]

1-3-3-4->[3,6,9,12]

1-3-3-7->[3,6,9,12,15,18,21]

1-3-6-1->[3]

1-3-6-4->[3,6,9,12]

1-3-6-7->[3,6,9,12,15,18,21]

1-3-6-10->[3,6,9,12,15,18,21,24,27,30]

1-3-6-13->[3,6,9,12,15,18,21,24,27,30,33,36,39]

1-3-6-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48]

1-3-9-1->[3]

1-3-9-4->[3,6,9,12]

1-3-9-7->[3,6,9,12,15,18,21]

1-3-9-10->[3,6,9,12,15,18,21,24,27,30]

1-3-9-13->[3,6,9,12,15,18,21,24,27,30,33,36,39]

1-3-9-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48]

1-3-9-19->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57]

1-3-9-22->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66 ]

1-3-9-25->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75].

Each path in the tree from the root node forms the initial terms of

a self-convolution cube of a sequence of integer terms.

Cf. A132852, A132854, A132855, A132856.

Cf. A083953, A132835.

Sequence in context: A111465 A108994 A006472 this_sequence A084879 A141118 A033030

Adjacent sequences: A132850 A132851 A132852 this_sequence A132854 A132855 A132856

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.