A132853 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution cube of an integer sequence such that 0 < c(n) <= 3*c(n-1) for n>0 with c(0)=1.

1, 1, 3, 18, 180, 4347, 245511, 33731424, 11850958449, 10823718435525, 26127739209077469, 169071160476526474689, 2962647736390311022542681, 141814999458311839862777779311, 18682218330844513414826192858258922

Offset: 0

Author

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

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Martin Fuller, Computing A132852, A132853, A132854, A132855, A132856

Crossrefs

Cf. A132852, A132854, A132855, A132856.

Cf. A083953, A132835.

Extensions

Extended by Martin Fuller, Sep 24 2007.