[seqfan] Re: A066411

[franktaw at netscape.net]

Great! Thanks, Ron.

There was a suggestion some time back that verification of values be 
noted in sequences; I think that is fully justified in this case. In 
the extensions area, put something like "Values a(0)..a(15) verified by 
...". I would also add the "nice" keyword.

It makes me wonder if the sequence is even monotonic. The smallest 
jumps seem to be happening at numbers of the form 2^k-1, which makes 
sense since those binomial coefficients are all odd, which determines 
the parity of the sum. Which means that 31 is the next likely case ... 
well beyond our ability to compute it, unless someone can get some 
theoretical insight.

Franklin T. Adams-Watters

-----Original Message-----
From: Ron Hardin <rhhardin at att.net>

I get 1 1 3 5 23 61 143 215 995 2481 5785 12907 29279 64963 144289 
158049 which
agrees with the series.

Time in C on a not very fast laptop for the last 3 terms

37h 30m
01h 33m
00h 05m

The method was representing it as a sum of a product of 0..n with 
binomial
coefficients,
sort the binomial coefficients smallest first,
apply the permutations of 0..15 to these in turn getting a cumulative 
sum at
each level,
look at each level L whether this set of L elements of 0..15 has been 
seen
before together with the same sum,
and if so abort further recursion at that level for that case.

I don't know if this implicitly takes into account all the symmetries 
talked
about.

One that sounds new is converting a n! problem into a 2^n problem, 
providing the

sums repeat, which is encouraged by taking the smallest coefficients 
first.

Remembering what has occurred already was subject to cache dumping at 
the
highest levels first, though I don't think that happened.

 rhhardin at mindspring.com
rhhardin at att.net (either)


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