[seqfan] Re: Moebius-transform of A005187 ?

Antti Karttunen antti.karttunen at gmail.com
Sat Mar 10 19:33:17 CET 2018


On Sat, Mar 10, 2018 at 8:10 PM, Antti Karttunen <antti.karttunen at gmail.com>
wrote:

>
> Consider the sequences A035532 and A297111:
>
> https://oeis.org/search?q=+%091%2C+2%2C+3%2C+4%2C+7%2C+4%
> 2C+10%2C+8%2C+12%2C+8%2C+18%2C+8%2C+22%2C+12&sort=&language=&go=Search
>
> The latter is Moebius-transform of A005187 I recently submitted, while
> from the formula-section of the former: G.f.: Sum A005187(n) x^n = Sum
> a(n)*x^n/(1-x^n)
> it seems to me that it also claims to be Möbius-transform of A005187. (See
> e.g. https://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula#
> Series_relations )
> However, the sequences differ for the first time at n=15, although even
> after that they seem to contain many identical terms.
>
> (Moreover, is there an indexing mismatch in Zumkeller's formula a(n) =
> 2*A000010(n) - A010051(n)*A048881(n) ?)
>
>
> Now, I just wonder where this "slightly flawed" insight in A035532 stems
> from, and on what specific n it fails: 15, 21, 25, 27, 33, 35, 51,  ...
> (where two sequences differ, "manually tallied" so beware) and why?
>
>
My own guess: The original author had computed only the initial 14 terms of
the sequence, then asked Superseeker or a similar program what else it
might be, and obtained the GF present in the formula-section.

Antti


>
> Best regards,
>
> Antti
>
>
>
>
>
>
>


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