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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. 5
1, 1, 6, 108, 7614, 2451762, 3773520918, 28927494486144, 1137959521626242430, 234471053096681379609150, 257075108927481255273258364890, 1518584605077301579030226106654776268, 48819910122176867311132781943952677374210562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..12.

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

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A127946 A012503 A168482 * A288629 A041149 A193810

Adjacent sequences:  A132853 A132854 A132855 * A132857 A132858 A132859

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Extended by Martin Fuller, Sep 24 2007

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)