[seqfan] Re: A179094

Douglas McNeil mcneil at hku.hk
Fri Aug 27 14:37:12 CEST 2010

[Aside: since 1 is odd and not even, I should've written the
conjectural formula as 'A179094(n) = 0 for n=1, n^3-n-1 for odd n > 1,
n^3-3 for even n.']

2010/8/27 Benoît Jubin:

> What would your program give when you also add the distance between
> the labels n^2 and 1 ? (0, 6, >=24, ...)

If I understand you then this is the round-trip variant, right?
Assuming I didn't break anything, I find

[   0    6   24   62  120  214  336  510  720  998 1320 1726 2184 2742 3360
 4094 4896 5830 6840]

which looks like a(1) = 0, a(n) = n^3-n for odd n > 1, a(n) = n^3-2 for even n.

> Also, can your program output the "winning configurations" for small n ?

Just to be clear, it's only my program in the sense that it's the
program that I used: namely, Concorde with glpk as the linear solver,
both of which can be freely downloaded, so the two groups get all the
props.  The methods are constructive so they'll output winning paths,
which can be converted into configurations and thus they provide
concrete evidence of the >= part, at least. :^)  Not sure what the
best way to store auxiliary data like that on the wiki will be.


Department of Earth Sciences
University of Hong Kong

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