# [seqfan] Re: A033791

David Newman davidsnewman at gmail.com
Thu Oct 16 03:16:52 CEST 2014

The sequence that I'm lookinh at is the number of partitions into summands
which are triangular numbers and frequencies satisfying the "no binary
carry" condition. A partition has the "no binary carry" condition if the
sum of all its frequencies, when written in binary notation has no carry.

On Wed, Oct 15, 2014 at 5:58 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> It would be easier to answer this question if you told us what your
> proposed sequence is.
>
>
>
> -----Original Message-----
> From: David Newman <davidsnewman at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Oct 15, 2014 4:52 pm
> Subject: [seqfan] Re: A033791
>
>
> The sequence that I'm working with will agree with A033791 for n<64, but
> will be different thereafter.  Should I propose it as new sequence or as a
> comment on A033791.
>
> On Wed, Oct 15, 2014 at 12:32 PM, Andrew N W Hone <A.N.W.Hone at kent.ac.uk>
> wrote:
>
>  Hi David,
>>
>> I am not looking at the sequence just now but I guess theta_2 is a
>>
> theta
>
>> function in Jacobi's classical notation: see
>>
>> http://en.wikipedia.org/wiki/Theta_function
>>
>> under "auxiliary functions". In the combinatorial setting, counting
>> partitions, you want to set the first argument z=0, which gives the
>>
> q-series
>
>>
>> \sum q^{(n+1/2)^2}
>>
>> where the sum is from n=-infinity to +infinity.
>>
>> A good classical reference is A Course of Modern Analysis by
>>
> Whittaker &
>
>> Watson. The first volume of Mumford's Tata Lectures on Theta is also
>>
> great,
>
>> and has a more modern point of view.
>>
>> All the best,
>> Andy
>>
>> ________________________________________
>> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of David
>>
> Newman [
>
>> davidsnewman at gmail.com]
>> Sent: 15 October 2014 17:23
>> To: Sequence Fanatics Discussion list
>> Subject: [seqfan] A033791
>>
>> I have a partition type sequence which matches A033791 for the first
>>
> 40
>
>> terms.  However, beyond the computational evidence I have no reason to
>> think that the two are the same.  In fact, I'm guessing that they
>>
> differ
>
>> for n>63.  I am hampered in my efforts  in part because I don't know
>>
> which
>
>> function is meant by theta2.  Could someone give me the definition of
>> theta2 or point me to a source for the definition?
>>
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