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

[jean-paul allouche]

Absolutely. If a(2n-1) = n^2 and a(k) nondecreasing, then
a(n) is equivalent to n^2/4.
jp


Le 27/02/2021 à 17:38, David Corneth a écrit :
>  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?
>>>>>>
>>>>> --
>>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>>>
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