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%I #35 Feb 14 2015 21:41:56
%S 1,4,57,2473,349712
%N Maximum value achievable for n X n version of Le Monde grid problem, using the original rules.
%C From Christian Boyer, Apr 18 2013: (Start)
%C 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.
%C With these rules, the new maximum for 3 X 3 is no longer 44, but 57:
%C 1 2 1
%C 3 7 30
%C 10 20 57
%C 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)
%D Eric Angelini and others, A Grid With MAX, Postings to the Math Fun Mailing List, April 14, 2013 onwards.
%D Christian Boyer, A Grid With MAX, Postings to the Math Fun Mailing List, April 18-25, 2013.
%H Le Monde, <a href="http://www.lemonde.fr/sciences/video/2013/04/12/les-defis-mathematiques-du-monde-episode-3-la-grille-de-sommes_3159020_1650684.html">Les défis mathématiques du "Monde", épisode 3 : la grille de sommes</a>
%e From Christian Boyer, Apr 25 2013: (Start)
%e a(5) = 349712: 1 7 11 33 33
%e 2 4 22 99 165
%e 1 30272 16581 286 550
%e 97477 67204 13662 2508 836
%e 349712 185031 6688 4180 836
%e a(6) >= 150941453:
%e 1 7 11 33 99 99
%e 2 4 22 66 297 495
%e 1 14105024 49432840 150941453 858 1650
%e 4574593 9530402 25797322 75705032 5016 2508
%e 2859120 1715472 381216 65208 22572 7524
%e 571824 571824 190608 125400 37620 7524
%e a(7) >= 164912612349.
%e a(8) >= 639561837115046.
%e (End)
%Y Cf. A224784.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Apr 18 2013
%E Value of a(5) and lower bounds for a(6)-a(8) corrected by Christian Boyer, Apr 25 2013
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