[seqfan] Re: A075681 and A003878

Neil Sloane njasloane at gmail.com
Thu Sep 10 01:29:20 CEST 2015


For A003878 I think the offset should simply be changed back to 0 (it was 0
in 1998)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Sep 9, 2015 at 7:10 PM, <israel at math.ubc.ca> wrote:

> What to do about these sequences?
>
> A003878's Name is n^4+(9/2)*n^3+n^2-(9/2)*n+1. The original Name was
> "Number of stacks of n pikelets, distance 4 flips from a well-ordered
> stack". Now the formula in the Name would imply a(0) to a(4) are 1, 3, 48,
> 199, 543, which are the first five numbers in Data, but the Offset is given
> as 3 which would make these a(3) to a(7). Is it safe to assume that Offset
> is just a mistake, and should be 0? The given g.f. also fits with an Offset
> of 0, rather than 3. I don't know about the "pikelet" interpretation though.
>
> A075681 is "Difference between (n-1)*(n-2)^3 and A003878." It is given as
> having offset 1 and Data starting 0, 0, 2, 21, 60, 121, 207, 321, and the
> Formula from Ralf Stephan is 1/2*n^3+7/2*n^2-23n+25 for n > 2. Well, Ralf's
> formula gives 6, -3, 1, 21, 60, 121, 207 for n = 1 .. 7. Moreover, the
> difference between (n-1)*(n-2)^3 and Ralf's formula is -6, 3, 1, 3, 48,
> 199, 543 for n = 1 .. 7. So, what do we make of this? The Data would fit
> with "Difference between (n-1)*(n-2)^3 and A003878" for n >= 4 if A003878
> keeps its current (presumably wrong) offset of 3. Should A075681(3) be 1
> instead of 2? Should we define A075681 in terms of A003878(n+3) if the
> offset of A003878 is changed to 0? Should we discard the two 0's and give
> A075681 an offset of 3? Does the current situation make sense in terms of
> the "flips" cryptically referred to in the Example?
>
> Cheers,
> Robert
>
>
>
>
>
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