[seqfan] NOT Re: Toroidal crossing number of K_n

Richard Guy rkg at cpsc.ucalgary.ca
Thu Mar 10 23:29:24 CET 2011

Noam & others,
               I've just recalled what I knew (and what is
not in OEIS) about that order 32 sequence, A139400.

It is the product of A001906 (alternate Fibs, x^2-3x+1),
A001353 (x^2-4x+1), A004253 (x^2-5x+1) and the fourth
order divisibility sequence 0, 1, 13, 132, 1261, ...
(x^4-13x^3+36x^2-13x+1), which is the sequence
(P1,P2,Q)=(13,34,1) in the Williams-Guy paper, so we
should give up looking for ranks of apparition, or, if
one DID wish to continue, then search these four
sequences and take the union of the results, but
evidently the complete theory exists for this
particular specimen.  But it's amazing that this
sequence, which occurs in real life, should be
composed of comparatively elementary sequences.   R.

On Wed, 9 Mar 2011, Noam Elkies wrote:

> Dear Richard,
> Hugh Williams inadvertently reminds me that I owe you and Matt
> a follow-up on divisibility sequences; I have some analogues of
> degree 8 and 12 whose possibility I realized soon after my previous
> communication on this topic but whose formulas I didn't get around to
> computing until just a few weeks ago.


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