0,3

Equals the number of nodes at generation n in the 2-convoluted tree. The minimal path in the 2-convoluted tree is A083952 and the maximal path is A132831. The 2-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 square of some integer sequence such that 0 < c(n) <= 2*c(n-1) for n>0 with a(0)=1.

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

Generations 0..5 of the 2-convoluted tree are as follows;

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

GEN.0: [1];

GEN.1: 1->[2];

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

GEN.3:

1-2-1->[2]

1-2-3->[2,4,6];

GEN.4:

1-2-1-2->[2,4]

1-2-3-2->[1,3]

1-2-3-4->[1,3,5,7]

1-2-3-6->[1,3,5,7,9,11];

GEN.5:

1-2-1-2-2->[2,4]

1-2-1-2-4->[2,4,6,8]

1-2-3-2-1->[2]

1-2-3-2-3->[2,4,6]

1-2-3-4-1->[2]

1-2-3-4-3->[2,4,6]

1-2-3-4-5->[2,4,6,8,10]

1-2-3-4-7->[2,4,6,8,10,12,14]

1-2-3-6-1->[2]

1-2-3-6-3->[2,4,6]

1-2-3-6-5->[2,4,6,8,10]

1-2-3-6-7->[2,4,6,8,10,12,14]

1-2-3-6-9->[2,4,6,8,10,12,14,16,18]

1-2-3-6-11->[2,4,6,8,10,12,14,16,18,20,22].

Each path in the tree from the root node forms the initial terms of a self-convolution square of a sequence with integer terms.

Cf. A132853, A132854, A132855, A132856.

Cf. A083952, A132831.

Sequence in context: A019537 A046911 A089127 this_sequence A055790 A020131 A032147

Adjacent sequences: A132849 A132850 A132851 this_sequence A132853 A132854 A132855

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.