login
A221866
Maximum value achievable for n X n version of Le Monde grid problem, using the original rules.
1
1, 4, 57, 2473, 349712
OFFSET
1,2
COMMENTS
From Christian Boyer, Apr 18 2013: (Start)
The beginning of this version of the game is different from that in A224784: now we start with 1's in two cells (not necessarily adjacent). After that the rules are the same: each new chosen cell is filled with the sum of the neighboring cells.
With these rules, the new maximum for 3 X 3 is no longer 44, but 57:
1 2 1
3 7 30
10 20 57
a(1) is no longer defined, but we set it equal to 1. a(2) and a(4) are the same as in A224784, but a(5)-a(8) are different. (End)
REFERENCES
Eric Angelini and others, A Grid With MAX, Postings to the Math Fun Mailing List, April 14, 2013 onwards.
Christian Boyer, A Grid With MAX, Postings to the Math Fun Mailing List, April 18-25, 2013.
EXAMPLE
From Christian Boyer, Apr 25 2013: (Start)
a(5) = 349712: 1 7 11 33 33
2 4 22 99 165
1 30272 16581 286 550
97477 67204 13662 2508 836
349712 185031 6688 4180 836
a(6) >= 150941453:
1 7 11 33 99 99
2 4 22 66 297 495
1 14105024 49432840 150941453 858 1650
4574593 9530402 25797322 75705032 5016 2508
2859120 1715472 381216 65208 22572 7524
571824 571824 190608 125400 37620 7524
a(7) >= 164912612349.
a(8) >= 639561837115046.
(End)
CROSSREFS
Cf. A224784.
Sequence in context: A231491 A240887 A209316 * A270881 A246618 A103907
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Apr 18 2013
EXTENSIONS
Value of a(5) and lower bounds for a(6)-a(8) corrected by Christian Boyer, Apr 25 2013
STATUS
approved