[seqfan] Re: The gerrymandering sequence A341578 needs better explanation

[David Corneth]

>From A341578: What is the asymptotic behavior of a(n)? - N. J. A. Sloane
<https://oeis.org/wiki/User:N._J._A._Sloane>, Feb 20 2021

We have a(2*n-1) = n^2 and a(k) <= a(k+1) so the asymptotic behaviour would
be a(n) = c*n^2 for some c right?


On Fri, Feb 26, 2021 at 7:37 PM Neil Sloane <njasloane at gmail.com> wrote:

> Andrew W., Jack G.,  Thank you very much for the clarification. I have
> revised A341578 accordingly.
>
> What is the asymptotic behavior of A341578(n)?  What is the sequence of d
> values?
>
> 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 Fri, Feb 26, 2021 at 7:13 AM Andrew Weimholt <andrew.weimholt at gmail.com
> >
> wrote:
>
> > It's not necessarily n districts with n votes each.
> >
> > For n=6, it is better to gerrymander the 36 votes into 3 districts with
> 12
> > votes each.
> >
> > In the former case, you'd need 15 votes to win: (4,4,4,3,0,0)
> > In the latter case, you'd only need 14: (7,7,0)
> >
> > Andrew
> >
> > On Fri, Feb 26, 2021 at 3:51 AM Jack Grahl <jack.grahl at gmail.com> wrote:
> >
> > > I think the confusing part is the 'grid'. This has essentially nothing
> to
> > > do with geometry.
> > >
> > > Given n districts, each with n votes, what is the least number of total
> > > votes which allows a party to win a majority of the districts?
> > >
> > > The districts are winner-takes-all, and for an even number of
> districts,
> > > it's enough to win half the districts, and tie in one further district.
> > >
> > > So for 5 districts of 5 votes, one party could theoretically win with 3
> > > votes in each of 3 districts, and 0 in all other districts. For 8
> > > districts, 5 votes in each of 4 districts, and 4 votes in a fifth
> > district
> > > is enough.
> > >
> > > On Fri, 26 Feb 2021, 10:47 Neil Sloane, <njasloane at gmail.com> wrote:
> > >
> > > > Typo, sorry. I meant to say:
> > > >
> > > > Dear Sequence Fans,  I had another look at A341578.  I accepted it
> > > because
> > > > some of the editors looked at it, and "gerrymandering" is an
> extremely
> > > > important topic.  But after looking at it more closely, I admit I
> don't
> > > > really understand the sequence.  Could someone explain the definition
> > > more
> > > > clearly?
> > > >
> > > >
> > > > On Fri, Feb 26, 2021 at 4:49 AM Neil Sloane <njasloane at gmail.com>
> > wrote:
> > > >
> > > > >
> > > > > Dear Sequence Fans,  I had another look at A3415678.  I accepted it
> > > > > because some of the editors looked at it, and "gerrymandering" is
> an
> > > > > extremely important topic.  But after looking at it more closely, I
> > > > admit I
> > > > > don't really understand the sequence.  Could someone explain the
> > > > definition
> > > > > more clearly?
> > > > >
> > > >
> > > > --
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> > > >
> > >
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> >
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