[seqfan] Re: Possible new sequences inspired by puzzles

[Charles Greathouse]

I think that both are worthy sequences, and likewise with the 3D extension.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Fri, Dec 28, 2012 at 11:33 AM, Dan Dima <dimad72 at gmail.com> wrote:

> Dear SeqFans,
>
> The following two related puzzles:
>
> http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/December2012.html
> http://www.brand.site.co.il/riddles/201212q.html
> might generate several sequences - the question is if they deserve a place
> in OEIS and also more terms are required:
>
> 1.
> Maximal sum of positive integers in a n x n grid such that if a natural
> number k is assigned then it must also have neighbors that have been
> assigned all of the numbers 1,2,...,k-1.
> (4 neighbors - 2 on the same row, 2 on the same column or less)
> 1, 7, 20, 39, a(5)=?, a(6)=93 as IBM Ponder This, a(7)=?
> There is no sequence in OEIS that matches this one ...
>
> This can be extended in 3-dimensional space as:
> Maximal sum of positive integers in a n x n x n grid such that if a natural
> number k is assigned then it must also have neighbors that have been
> assigned all of the numbers 1,2,...,k-1.
> (6 neighbors or less)
> 1, 20, ...
>
> 2.
> Maximal sum of positive integers in a n-dimensional hypercube (2 x 2 x ....
> x 2 n-times) such that if a natural number k is assigned to a vertex then
> it must also have adjacent vertices that have been assigned all of the
> numbers 1,2,...,k-1.  (n neighbors)
> 3, 7, 20, ...
>
> Best Regards,
> Dan
>
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