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A132855 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 5th power of an integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with c(0)=1. 5
1, 1, 5, 75, 3625, 638750, 442823125, 1278820631250, 15775429658296875, 848938273203627578125, 202483260558673741179296875, 216741216953142470752123517187500, 1051774892873652266440974611041742187500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The minimal path in the 5-convoluted tree is A083955 and the maximal path is A132839.

Equals the number of nodes at generation n in the 5-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 5th power of some integer sequence such that 0 < c(n) <= 5*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 5-convoluted tree are as follows;

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

GEN.0: [1];

GEN.1: 1->[5];

GEN.2: 1-5->[5,10,15,20,25];

GEN.3:

1-5-5->[5,10,15,20,25]

1-5-10->[5,10,15,20,25,30,35,40,45,50]

1-5-15->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75]

1-5-20->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100]

1-5-25->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105, 110,115,120,125].

Each path in the tree from the root node forms the initial terms of a self-convolution 5th power of a sequence of integer terms.

CROSSREFS

Cf. A132852, A132853, A132854, A132856; A083955, A132839.

Sequence in context: A091882 A034688 A238608 * A238560 A303125 A332714

Adjacent sequences:  A132852 A132853 A132854 * A132856 A132857 A132858

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 29 09:35 EST 2020. Contains 332355 sequences. (Running on oeis4.)