A221866 Maximum value achievable for n X n version of Le Monde grid problem, using the original rules.

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.

Links

Table of n, a(n) for n=1..5.

Le Monde, Les défis mathématiques du "Monde", épisode 3 : la grille de sommes

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

Adjacent sequences: A221863 A221864 A221865 * A221867 A221868 A221869

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