Why isn't 0 in A034710?

[N. J. A. Sloane]

Martin (and Seqfans), 
     Wow, thanks for all the superb work on the extensions/corrections! 
Would you have the further energy to submit these corrections? 
  
I have already submitted the main sequences, but have re-numbered them!  
And changed the name to reflect my motivation in researching them. 
  
Below I copy the new A-numbers - sorry if this caused any confusion. 
  
Also, I have not submitted the corresponding trees (due to seeming lack
of interest).  
  
Further, a table enumerating the k-convoluted trees would be nice -- 
where the counts of the k-convoluted tree at k=1 is defined as all '1's, 
and could form row 1 (or column 1) of the table. 
If you are so inclined, perhaps you would like to submit the table. 
  
I have reserved the following A-numbers for further sequences along these
lines
(not yet used):
 
A132850 - Square array, read by antidiagonals, enumerating k-convoluted
trees.
A132851 - Main diagonal of table A132850. 
  
A132857 
A132858 
A132859 
A132860 
 
Thanks again! 
     Paul 
  
SUBMITTED and available in OEIS:
 
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. 
 
A132853 - 
Number of sequences {c(i), i=0..n} that form the initial terms of a
self-convolution cube of an integer sequence such that 0 < c(n) <=
3*c(n-1) for n>0 with c(0)=1. 
 
A132854 - 
Number of sequences {c(i), i=0..n} that form the initial terms of a
self-convolution 4-th power of an integer sequence such that 0 < c(n) <=
4*c(n-1) for n>0 with c(0)=1. 
 
A132855 - 
Number of sequences {c(i), i=0..n} that form the initial terms of a
self-convolution 5-th power of an integer sequence such that 0 < c(n) <=
5*c(n-1) for n>0 with c(0)=1. 
 
A132856 - 
Number of sequences {c(i), i=0..n} that form the initial terms of a
self-convolution 6-th power of an integer sequence such that 0 < c(n) <=
6*c(n-1) for n>0 with c(0)=1. 
 


On Tue, 25 Sep 2007 00:27:13 +0100 (BST) Martin Fuller
<martin_n_fuller at btinternet.com> writes:
> Paul, seqfans,
> 
> I have attached a PARI program (with explanation) which I used to
> generate the values below. They match your calculations except for 
> the
> 6th and 7th terms of A132855.
> 
> A132851: 
> Number of nodes at generation n in the 2-convoluted tree (A132850). 
> 1, 1, 2, 4, 14, 62, 462, 5380, 105626, 3440686, 196429906, 
> 19603795552,
> 3496015313038, 1120368106124268, 653253602487886098,
> 697073727912597623594, 1371575342274982257650434,
> 5001872822460132255638199998, 33985054727503111175373886399250,
> 432024026653870819584750328953621778
> 
> A132853: 
> Number of nodes at generation n in the 3-convoluted tree (A132852). 
> 1, 1, 3, 18, 180, 4347, 245511, 33731424, 11850958449, 
> 10823718435525,
> 26127739209077469, 169071160476526474689, 2962647736390311022542681,
> 141814999458311839862777779311, 18682218330844513414826192858258922,
> 6816346360277755893118363665630012225420
> 
> A132855: 
> Number of nodes at generation n in the 4-convoluted tree (A132854). 
> 1, 1, 4, 32, 736, 47600, 9901728, 6780161344, 15819971230848,
> 128391245362464512, 3685238521747987153664,
> 378871127417706380405937152, 140962622184196263047081802452992,
> 191428155805533938524028481989647915008,
> 955702499453836874538617308649867009480896512
> 
> A132857: 
> Number of nodes at generation n in the 5-convoluted tree (A132856). 
> 1, 1, 5, 75, 3625, 638750, 442823125, 1278820631250, 
> 15775429658296875,
> 848938273203627578125, 202483260558673741179296875,
> 216741216953142470752123517187500,
> 1051774892873652266440974611041742187500,
> 23332485704169236846450189449001711184697265625
> 
> A132859: 
> Number of nodes at generation n in the 6-convoluted tree (A132858). 
> 1, 1, 6, 108, 7614, 2451762, 3773520918, 28927494486144,
> 1137959521626242430, 234471053096681379609150,
> 257075108927481255273258364890, 
> 1518584605077301579030226106654776268,
> 2176867311132781943952677374210562,
> 8612868429525484388625401466547224861259048650708888
> 
> Martin Fuller
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20070924/9506c77a/attachment-0001.htm>