Riffs & Rotes & A061396

[Jon Awbrey]

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David W. Wilson wrote:
> 
> Jon Awbrey wrote:
> >
> > [stuff omitted]
> >
> > Vladeta Jovovic wrote:
> > >
> > > Dear Jon Awbrey,
> > >
> > > Welcome to SeqFan community!
> > >
> > > I tried  to calculate your seq. A061396 and got:
> > >
> > > 1, 1, 2, 6, 20, 73, 281, 1124, 4618,
> > > 19387, 82765, 358245, 1568458, 6933765,
> > > 30907194, 138760603, 626898401, 2847946941,
> > > 13001772692, 59618918444, 274463781371,
> > > 1268064807409, 5877758070220, 27325789128330,
> > > 127384553264327, 595318139942874, 2788598203340643,
> > > 13090395266913748, 61571972632103632, 290146443773731410,
> > > 1369624976703419031
> > >
> > > My calculation for a(8) gives 4618.
> > >
> > > Best wishes,
> > > Vladeta Jovovic
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > David W. Wilson wrote:
> > >
> > > I computed this sequence from the g.f.  I get
> > >
> > > 1, 1, 2, 6, 20, 73, 281, 1124, 4618,
> > > 19387, 82765, 358245, 1568458, 6933765,
> > > 30907194, 138760603, 626898401, 2847946941,
> > > 13001772692, 59618918447 *, 274463781383 *,
> > > 1268064807513 *, 5877758071073 *, 27325789133590 *,
> > > 127384553287387 *, 595318140045752 *
> > >
> > > [etc]
> 
> I did my calculations in Perl, which apparently has a problem
> with 64-bit arithmetic.  I redid the calculation in C++, and
> my results now corroborate Vladeta's.  Use his sequence:
> 
> 1, 1, 2, 6, 20, 73, 281, 1124, 4618,
> 19387, 82765, 358245, 1568458, 6933765,
> 30907194, 138760603, 626898401, 2847946941,
> 13001772692, 59618918444, 274463781371,
> 1268064807409, 5877758070220, 27325789128330,
> 127384553264327, 595318139942874, 2788598203340643,
> 13090395266913748, 61571972632103632, 290146443773731410,
> 1369624976703419031

Thanks, David and Vladeta, that restores my faith in mathematics --
speaking of which, now that I have given a better description of
these classes of structures, I hope that some fresh gray cells
might be recruited to check that purported proof sketch in
my first note to see if they think it is adequate.

Thanks In Prospect,

Jon Awbrey

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