Riffs & Rotes & A061396

[Jon Awbrey]

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David,

This is super!  I got an off-list message on this
from Vladeta Jovovic earlier today, and I do not
think that it would be inappropriate to cite my
response here, by way of extending my thanks to
you and allowing you both to compare results.

I inserted commas -- for the sake of these old eyes --
and I marked with asterisks the places where a few
differences start to appear.

Sequential Gratitude,

Jon Awbrey

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Dear Vladeta Jovovic,

Gosh, that's really beautiful!
Did you get all of that from the
generating function?  Mathematica?
I knew that things had progressed
since those days, but this is
really something.  Yes, it is
very likely that I could have
miscounted, as I was working
from a couple of very ugly
formulas.  If you can read
a Word Doc, I could send
the ones that I have and
you could check them for
their validity or not.
Probably you should
report this back to
Neil and the list.

Many Regards,

Jon Awbrey

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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

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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 *
> 
> My a(8) = 4618 disagrees with the published a(8) = 4488.  I computed the
> sequence using two programs, with the same result, and I am pretty sure
> it is correct (some corroboration would be welcomed).  In defense of my
> value, notice that the relative differences of my terms increase nicely:
> 
>                1/1                = 1.000000
>                2/1                = 2.000000
>                6/2                = 3.000000
>               20/6                = 3.333333
>               73/20               = 3.650000
>              281/73               = 3.849315
>             1124/281              = 4.000000
>             4618/1124             = 4.108541
>            19387/4618             = 4.198138
>            82765/19387            = 4.269098
>           358245/82765            = 4.328460
>          1568458/358245           = 4.378171
>          6933765/1568458          = 4.420753
>         30907194/6933765          = 4.457491
> 
> whereas a(8) = 4488 produces a sudden decrease of the relative difference,
> which would be unexpected in this context.
> 
>                1/1                = 1.000000
>                2/1                = 2.000000
>                6/2                = 3.000000
>               20/6                = 3.333333
>               73/20               = 3.650000
>              281/73               = 3.849315
>             1124/281              = 4.000000
>             4488/1124             = 3.992883

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