[seqfan] Re: integer sequence that is the sum of two or more known integer sequences

[Brad Klee]

Hi Craig,

I recently did something like this for various sequences derived from Molien series. I was able to find many relations w/ a brute force approach.

First I generate 20 or 30 terms for all sequences, then I generate a space of integer coefficients for the partial sequences and create one partial sequence for each set of coefficients by multiplying and summing.

Once candidate sequence fragments are generated, I use Mathematica to query OEIS with the numbers then parse the results to list A numbers.

Finally, I compare generating functions to ensure that the sequences are the same.

This approach begins to find the elements belonging to the vector space spanned by some finite basis.

Classifying vector spaces is better than finding linear relations because the belonging of a vector to a vector space implies many linear relations especially when the vector space contains many inequivalent spanning sets. For example ~20-30 Molien belongings imply hundreds to thousands of linear relations.

Taking a space approach you have more complicated questions such as: given two vector spaces do they intersect, if so how?

I'm not sure you want to limit yourself to basis dependent search, but you could get some results this way.

I can send you my Mathematica notebooks on the Molien search if you are interested.

Cheers,

Brad

> On Jul 8, 2015, at 10:00 AM, Craig Knecht <craigknecht03 at gmail.com> wrote:
> 
> Is there a way to sort the data base to find all integers sequences that
> are stated to be the sum of other integer sequences?
> The percentage of the total would be of some interest. I also have a idea
> of trying to reverse engineer a sequence based on such data.
> 
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