A132856 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 6th power of an integer sequence such that 0 < c(n) <= 6*c(n-1) for n>0 with c(0)=1.

1, 1, 6, 108, 7614, 2451762, 3773520918, 28927494486144, 1137959521626242430, 234471053096681379609150, 257075108927481255273258364890, 1518584605077301579030226106654776268, 48819910122176867311132781943952677374210562

Offset: 0

Author

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

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Extensions

Extended by Martin Fuller, Sep 24 2007