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A132852 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution square of an integer sequence such that 0 < c(n) <= 2*c(n-1) for n>0 with c(0)=1. 5
1, 1, 2, 4, 14, 62, 462, 5380, 105626, 3440686, 196429906, 19603795552, 3496015313038, 1120368106124268, 653253602487886098, 697073727912597623594, 1371575342274982257650434 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..16.

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

EXAMPLE

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.

CROSSREFS

Cf. A132853, A132854, A132855, A132856.

Cf. A083952, A132831.

Sequence in context: A019537 A046911 A089127 * A132079 A055790 A322623

Adjacent sequences:  A132849 A132850 A132851 * A132853 A132854 A132855

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 January 21 11:11 EST 2020. Contains 331105 sequences. (Running on oeis4.)