%I
%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 selfconvolution square of an integer sequence such that 0 < c(n) <= 2*c(n1) for n>0 with c(0)=1.
%C Equals the number of nodes at generation n in the 2convoluted tree. The minimal path in the 2convoluted tree is A083952 and the maximal path is A132831. The 2convoluted tree is defined as follows: tree of all finite sequences {c(k), k=0..n} that form the initial terms of a selfconvolution square of some integer sequence such that 0 < c(n) <= 2*c(n1) 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 2convoluted 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: 12>[1,3];
%e GEN.3:
%e 121>[2]
%e 123>[2,4,6];
%e GEN.4:
%e 1212>[2,4]
%e 1232>[1,3]
%e 1234>[1,3,5,7]
%e 1236>[1,3,5,7,9,11];
%e GEN.5:
%e 12122>[2,4]
%e 12124>[2,4,6,8]
%e 12321>[2]
%e 12323>[2,4,6]
%e 12341>[2]
%e 12343>[2,4,6]
%e 12345>[2,4,6,8,10]
%e 12347>[2,4,6,8,10,12,14]
%e 12361>[2]
%e 12363>[2,4,6]
%e 12365>[2,4,6,8,10]
%e 12367>[2,4,6,8,10,12,14]
%e 12369>[2,4,6,8,10,12,14,16,18]
%e 123611>[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 selfconvolution 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.
