A132856 - OEIS

%I #11 Mar 13 2015 00:48:27

%S 1,1,6,108,7614,2451762,3773520918,28927494486144,1137959521626242430,

%T 234471053096681379609150,257075108927481255273258364890,

%U 1518584605077301579030226106654776268,48819910122176867311132781943952677374210562

%N 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.

%C The minimal path in the 5-convoluted tree is A083956.

%C 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.

%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..3 of the 6-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->[6];

%e GEN.2: 1-6->[3,9,15,21,27,33];

%e GEN.3:

%e 1-6-3->[2,8,14]

%e 1-6-9->[2,8,14,20,26,32,38,44,50]

%e 1-6-15->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86]

%e 1-6-21->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122]

%e 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]

%e 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].

%e 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.

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 19 2007, Oct 06 2007

%E Extended by _Martin Fuller_, Sep 24 2007