

A221866


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


1




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 1825, 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



