need help with recent "uned" seqs - A082219: square w/ partial sums multiple of n

[Max Alekseyev]

On 6/11/07, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> Max,
> I saw you added very recently numbers to the following sequence:
>
> %N A082219 In the following square array, numbers (not occurring
> earlier) are entered like this:
> a(1,1)=1,a(1,2),a(2,1),a(3,1),a(2,2)... such that every n-th partial
> sum of a row or a column is a multiple of n.  Sequence contains the
> first  row.
>
> But it is still "uned" and "more".
> * do you think it should remain "more" ? I somehow think that it's
> mainly the counter-conventional filling-in method that makes it
> nontrivial.

I think that it does not require "more" flag anymore.
But I have no control over it, I have just sent Neil extension of this
sequence (and related seqeunces A082220-A082223). I was hoping that
Neil would drop "more" flag.

> Did you find the numbers by hand or with an intelligent algorithm or
> with a less intelligent brute-force PARI code ?

My code is rather straightforward:

{ A082219() =
a=matrix(1000,1000);
S=Set();
for(s=2,1001, if(s%2,i0=1;i1=s-1;i2=1,i0=s-1;i1=1;i2=-1); forstep(i=i0,i1,i2,
j=s-i;
ii=sum(k=1,j-1,a[i,k]); jj=sum(k=1,i-1,a[k,j]);
c=chinese(Mod(ii,j),Mod(jj,i));
t=component(c,1)-lift(c); while(setsearch(S,t),t+=component(c,1));
a[i,j]=t;
S=setunion(S,[t]);
if(i==1, print1(", ",sum(k=1,j,a[i,j])/j) );
))
}

> * would you agree that my shortended %N entry contains all essential
> information (the current %N is at least twice as long) - this would
> already be a first editorial step... maybe better :
> %N A082219 First row of square array filled with numbers (not
> occurring earlier) according to:
> a(1,1)=1,a(1,2),a(2,1),a(3,1),a(2,2)... such that every n-th partial
> sum of a row or a column is a multiple of n.

I have no objections, except that "and" should be used instead of "or":

"...such that every n-th partial sum of every row and every column is
a multiple of n"

sounds slightly better to me.

Also, maybe, we should give a standard name to such "zigzag"
enumeration of rectangular arrays and define it in the OEIS
documentation (if not yet). That would shorten the name of this and
similar sequences. Instead of defining the filling order in %N field
they may simply mention this (whatever) "zigzag" name and refer to the
appropriate place in the OEIS documentation in %C or %H field.

Regards,
Max



Maximilian, Max:  thanks for reminding me that A082219-A082223
Neil