Various items

[N. J. A. Sloane]

1. I am back from Holland and have caught up with submissions
that arrived while I was away. There were 2637 new messages waiting
when I returned, so i was not able to reply to every one individually.
In particular, I silently rejected several submissions.

2. A puzzle, answer not known:
%I A092827
%S A092827 3,10,16,17,64,14,121,11,25
%N A092827 From a quiz. The choices given for the next two terms are: i) 12,32; ii) 22,18; iii) 17,64; iv) 5,21; v) 13,19.
%K A092827 nonn,unkn,more,new
%O A092827 1,1
%A A092827 Madhav Narayanan (madhav.narayanan(AT)iiitb.ac.in), Apr 15 2004

3. Amarnath Murthy has submitted a lot of new sequences, many of which
I edited. But after I while I got tired of making
the same corrections over and over, so I just marked them
with the keyword "uned", meaning "unedited".
It would be nice if the associate editors or other seqfans
would help edit them (or recommend that they be rejected - "uned" 
also means "on probation").  Sequences A093905-A093921 among others
need editing.

4. Sequences needed from theta series of lattices:
The lattice database that G. Nebe and I maintain,
http://www.research.att.com/~njas/lattices/index.html
contains a large number of lattices. It would be nice if the OEIS
contained all the theta series of these lattices, but at presemt a lot 
are missing. Maybe people could help send them in.
There are plenty to work on!

Example: The lattice D_4. The theta series is Sum_{x in lattice } q^(x.x),

- in other words, Sum q^{ squared length of vector} -

which in this case is 

1 + 24*q^2 + 24*q^4 + 96*q^6 + 24*q^8 + 144*q^10 + 96*q^12 + ...

If we simply list the coefficients we get

1, 0, 24, 0, 24, 0, 96, 0, 24, 0, 144, 0, 96, 0, 192, 0, 24, 0, 312,  ...

but the convention is that we get rid of those alternate 0's, that is,
we replace q by q^(1/k) where k is as large as possible, in this case 2, getting

1 + 24*q + 24*q^2 + 96*q^3 + 24*q^4 + 144*q^5 + 96*q^6 + 192*q^7 + 24*q^8 + ...

i.e.  1, 24, 24, 96, 24, 144, 96, 192, 24, 312, ...

which gives A004011:

%I A004011 M5140
%S A004011 1,24,24,96,24,144,96,192,24,312,144,288,96,336,192,576,24,432,312,480,
%T A004011 144,768,288,576,96,744,336,960,192,720,576,768,24,1152,432,1152,312,
%U A004011 912,480,1344,144,1008,768,1056,288,1872,576,1152,96,1368,744,1728,336
%N A004011 Theta series of D_4 lattice; Fourier coefficients of Eisenstein series E_{gamma,2
}.
%C A004011 E_{gamma,2} is the unique normalized modular form for Gamma_0(2) of weight 2.
%D A004011 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springe
r-Verlag, p. 119.
%H A004011 B. Brent, <a href="http://www.expmath.org/expmath/volumes/7/7.html">Quadratic Min
ima and Modular Forms, Experimental Mathematics, v.7 no.3, 257-274.</a>
%H A004011 Michael Gilleland, <a href="http://www.research.att.com/~njas/sequences/selfsimil
ar.html">Some Self-Similar Integer Sequences</a>
%H A004011 G. Nebe and N. J. A. sloane, G. Nebe and N. J. A. Sloane, <a href="http://www.res
earch.att.com/~njas/lattices/D4.html">Home page for D_4 lattice</a>
....

So that one IS in the OEIS.  But there are probably hundreds that are not.
There are many ways to compute the theta series - I can supply
more information if anyone needs it.

5. On May 4 at 4pm I'm talking about the OEIS in The DIMACS Center at Rutgers.

End of report!

Neil