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%I #6 Apr 03 2014 11:35:08
%S 1,1,2,4,14,62,462,5380,105626,3440686,196429906,19603795552,
%T 3496015313038,1120368106124268,653253602487886098,
%U 697073727912597623594,1371575342274982257650434
%N 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.
%C 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.
%H Martin Fuller, <a href="/A132852/a132852.txt">Computing A132852, A132853, A132854, A132855, A132856</a>
%e a(n) counts the nodes in generation n of the following tree.
%e Generations 0..5 of the 2-convoluted tree are as follows;
%e The path from the root is shown, with child nodes enclosed in [].
%e GEN.0: [1];
%e GEN.1: 1->[2];
%e GEN.2: 1-2->[1,3];
%e GEN.3:
%e 1-2-1->[2]
%e 1-2-3->[2,4,6];
%e GEN.4:
%e 1-2-1-2->[2,4]
%e 1-2-3-2->[1,3]
%e 1-2-3-4->[1,3,5,7]
%e 1-2-3-6->[1,3,5,7,9,11];
%e GEN.5:
%e 1-2-1-2-2->[2,4]
%e 1-2-1-2-4->[2,4,6,8]
%e 1-2-3-2-1->[2]
%e 1-2-3-2-3->[2,4,6]
%e 1-2-3-4-1->[2]
%e 1-2-3-4-3->[2,4,6]
%e 1-2-3-4-5->[2,4,6,8,10]
%e 1-2-3-4-7->[2,4,6,8,10,12,14]
%e 1-2-3-6-1->[2]
%e 1-2-3-6-3->[2,4,6]
%e 1-2-3-6-5->[2,4,6,8,10]
%e 1-2-3-6-7->[2,4,6,8,10,12,14]
%e 1-2-3-6-9->[2,4,6,8,10,12,14,16,18]
%e 1-2-3-6-11->[2,4,6,8,10,12,14,16,18,20,22].
%e Each path in the tree from the root node forms the initial terms of a self-convolution square of a sequence with integer terms.
%Y Cf. A132853, A132854, A132855, A132856.
%Y Cf. A083952, A132831.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 19 2007, Oct 06 2007
%E Extended by _Martin Fuller_, Sep 24 2007.
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