[seqfan] Re: Nice new seq needs a formula

[Neil Sloane]

To get the offsets to match, the conjecture is that

A306302(n) =  n + (A114043(n+1)-1)/2

E.g. 46 = 3 + (87-1)/2.


On Thu, Feb 7, 2019 at 5:08 PM Neil Sloane <njasloane at gmail.com> wrote:

> The new sequence that I mentioned , A306302(n),
> appears to equal n + (A114043(n)-1)/2, and A114043 has an explicit formula
> due to Max Alekseyev.  The two sequences A306302 and A114043
> are sufficiently similar that it should not be hard to find a proof.
>
> (Thanks to Superseeker for the hint).
>
>
> 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 Thu, Feb 7, 2019 at 1:26 PM Hugo Pfoertner <yae9911 at gmail.com> wrote:
>
>> Links to available literature for this problem are given in
>> http://oeis.org/A288177
>> http://oeis.org/A306302 is part of the triangle http://oeis.org/A288187
>> If more terms can be found - fine, but we shouldn't re-invent the reseach
>> done by Pfetsch, Ziegler and others 15 years ago.
>>
>> Hugo Pfoertner
>>
>> On Thu, Feb 7, 2019 at 7:16 PM Neil Sloane <njasloane at gmail.com> wrote:
>>
>> > PS and what about the numbers of vertices (including both boundary
>> points
>> > and interior intersection points)?
>> >
>> >
>> > On Thu, Feb 7, 2019 at 1:09 PM Neil Sloane <njasloane at gmail.com> wrote:
>> >
>> > > No of regions in a strip of rectangles:  A306302
>> > >
>> > > Given enough terms, will probably be guessable
>> > > 4, 16, 46, 104, 214 is not enough
>> > >
>> > >
>> > >
>> >
>> > --
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>> >
>>
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>