[seqfan] Re: definition of A002848

[franktaw at netscape.net]

I beg to differ.  I wrote:

"Possibly (I haven't really checked, but the pattern is right) A002849
is the number of partitions of a subset of 1..n into triples X+Y=Z,
with the maximum possible number of such triples.  A002848 would then
be the number of such partitions that include n in one of the triples.

"If this is correct, I would argue that A002849(1) and A002849(2) 
should
both be 1, representing the empty partition."

Using the following PARI program:

nxyz(v,t)={local(n,r,x2);r=0;
 if(t==0,return(1));
 for(i3=3*t,#v,
  n=v[i3];
  for(i1=1,i3-2,
   x2=n-v[i1];
   if(x2<=v[i1],break);
   for(i2=i1+1,i3-1,
    if(v[i2]>=x2,
     if(v[i2]==x2,
      r+=nxyz(vector(i3-3,k,v[if(k<i1,k,if(k<i2-1,k+1,k+2))]),t-1));
     break))));
 r}

a(n)=nxyz(vector(n,k,k),n\3-(n%12==6|n%12==9))

I match A002849 except for a(1) and a(2), mentioned above, and a(14) 
for which I get 204 instead of 202; this exception was noted by Alois 
Heinz in his post.

The sequence then continues with:

135, 1002, 4228, 720, 5134, 29546, 4079

A002848(n) is A002849(n) for n == 0,3,7,10 (mod 12), 0 for n=1, and 
A002849(n)-A002849(n-1) otherwise.

Franklin T. Adams-Watters

-----Original Message-----
From: N. J. A. Sloane <njas at research.att.com>

Dear Sequence Fans,  I will rewrite the definitions
of A002848 and A002849 to give more information

The various guesses that were made here were not right!

Neil