interview (podcast) about the OEIS

[N. J. A. Sloane]

It appears to me that A049597, taken with offset 1 instead of 0,
has a combinatorial interpretation as the number of partitions of n
with #parts + largest part - 1 equal to k.  Looking at the Ferrers
diagram, this is the number of dots in the first row or the first
column.  This would make A083480 (taking the first term to be
A083480(1,0)) the number of partitions of n with k dots not on
the first row or column of the Ferrers diagram.  In which case we
have A083480(1,k) = 1 for k = 0, otherwise 0, A083480(n,n) = 0
for n>1, and for n > k > 0,

A083480(n,k) = A083480(n-1,k) + Sum_{i>=2k-n-2} A083480(k,i).

(Here A083480(n,k) is taken to be 0 if k < 0.)  (This formula is
easily derived by looking at the number of dots required to embed
a partition in the "interior" of the Ferrers diagram, plus the number
of ways that this can be extended by adding dots to the first row
and column.)  Equivalently, we get

A083480(n,k) = 2 A083480(n-1,k) - A083480(n-2,k) + A083480(k,2k-n+2),

with the same boundary conditions plus A083480(0,k) = 0.

The latter formula is equivalent to

A049597(n,k) = 2 A049597(n-1,k-1) - A049597(n-2,k-2) + A049597(n-k,k-2),

with appropriate boundary conditions.

This correspondence would also imply the correctness of the conjecture 
in
A083480 for the number of terms in each row.

As it happens, I have a copy of the book by Andrews referenced in 
A049597,
but I can't find it right now.  This might be a good place to look 
first.  The
identities above might be verified by comparison with the programs by 
Emeric
in A049597 and A083480.  I might try this if I get ambitious.

Franklin T. Adams-Watters



Two options that may make additional work smaller are

1) (zero work, only setup)
If comments or updates are pending than a link
could show up in the sequence that points to the
unprocessed input.

2) bugzilla
Very neat and structured system, but may lead
to extra work because 'bug' needs to be closed
after update is done.  However, I seem to recall
that bugzilla is extremely adaptable and the
extra work may be essentially zero.

Some good things about (2):
Editors of the database can independently work
on stuff (dunno how it works now) and contributors
can fix their stuff if needed.  So this solution
may _lower_ the workload for Neil!

If a contribution is unclear or has issues
the bug can just be reassigned to the submitter

And one can point to the bugzilla entry if the
So Neil does not need to search morsels in the list.

Also declined changes are documented and duplicate
discussions are avoided.

It may be a good idea to feed the contributions arriving in
the way used now (web form and mail) into bugzilla.


Note (1) and (2) would work nicely together.


Just my 0.02 Australian dollar


* N. J. A. Sloane <njas at research.att.com> [May 08. 2008 19:49]:
> 
> Dear Seqfans,  I think the idea of a wiki about the OEIS
> is a terrible one.  It would inevitably produce two
> versions of sequences, and it would make my job even harder
> than it is now.
> 
> 
> One argument that was mentioned was that there one
> could give discussions of ambiguous terms (such as
> proper divisor).  But that can be handled by entries
> in the Index.  I'm adding an entry for 
> divisor, proper
> now
> 
> 
>  Best regards
>  			 Neil




%I A000720
%S A000720 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9
%C A000720 Plouffe's conjecture for the OGF is wrong, see the following pari/gp code:
N=50;
v1=Vec(s)
v2=vector(N,j,primepi(j+1))
v1-v2
%o A000720 (PARI) vector(300,j,primepi(j))
%O A000720 1
%K A000720 ,nonn,
%A A000720 Joerg Arndt (arndt at jjj.de), May 09 2008
RH 
RA 192.20.225.32
RU 
RI 

The pari/gp sessions is:

? N=50;
? s=-z*(-1-z-z^3-z^5+z^6+z^7)/(1+z)/(z^2-z+1)/(z^2+z+1)/(z-1)^2;
? s+=O(z^(N+1))
z + 2*z^2 + 2*z^3 + 3*z^4 + [...]
? v1=Vec(s)
[1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, ...]
? v2=vector(N,j,primepi(j+1))
[1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, ...]
? v1-v2
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,