[seqfan] Re: A066411

[William Keith]

On Tue, Jan 24, 2012 at 6:22 AM, <franktaw at netscape.net> wrote:

> The last published value of this sequence - a(15) - looks suspicious. For
> all previous n>1, a(n) / a(n-1) > 3/2; for this it is only about 1.1. I
> suspect that some kind of overflow occurred in the calculation, though I am
> by no means sure. Can someone check the value?
>
> Franklin T. Adams-Watters
>

An attempt at brute force calculation of a(15) did indeed throw an overflow
error.  Since there are an even number of terms in {0,...,15}, and there is
no "interference" between the two sides, I could suggest that one way to
keep down the amount of working memory is to:

1.) take 8-element subsets of {0,...,14} (there are 6435), and their
15-complement, i.e. {15-a_k}
2.) take the 40320 permutations of each subset and its complement
3.) Construct the sums a_k*Binomial[15,k] for each half, and add them
4.) Keep a running tally of distinct sums.

This isn't very fast, of course.  I can't think of a cute recurrence to
help with this calculation.

William Keith