[seqfan] Possible new sequences inspired by puzzles

[Dan Dima]

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