[seqfan] Re: A179094

Douglas McNeil mcneil at hku.hk
Thu Aug 26 13:02:56 CEST 2010


> If I'm reading my notes correctly I find 0, 5, 23, >=61, >=119, >=212,
>>= 335, >= 507, >= 719, >= 993 but those could be pretty loose.  It'd
> be nice to have at least fourth known term, as you can get 0 and 5 by
> inspection..  Any takers with a good TSP code?

After tweaking the example in the package, glpk reports that 61, 119,
and 719 are optimal.  After getting the Concorde code to compile with
glpk (credits to Applegate et al. and Makhorin), I find that A179094
begins:

1 0
2 5
3 23
4 61
5 119
6 213
7 335
8 509
9 719
10 997
11 1319
12 1725
13 2183
14 2741
15 3359
16 4093
17 4895
18 ?
19 6839
20 ?
21 9239
22 ?
23 12143

Plotting shows it's almost exactly a cube, so after some fiddling I
conjecture that

A179094(n) = 0 for n=1, n^3-3 for even n > 0, n^3-n-1 for odd n.

but trusting my use of two codes I've used for the first time is a
dangerous plan.  Confirmation, counterexamples, or slick arguments
showing the answer was obvious all gratefully received!  A superseeker
request is pending; we'll see what it says.


Doug

-- 
Department of Earth Sciences
University of Hong Kong




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