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%I #29 Jan 31 2024 08:03:58
%S 0,180,16352,3932100,3221225376,9620726742900,108086391056891712,
%T 4648579506574807006980,773712524553362671811952320,
%U 501989637690378842992694469328500,1276058875953519237987654777869130792480,12756026253559516436958430851954862781420797380
%N Maximum score achievable in the 2048 game on an n X n grid.
%C This sequence is based on the original 2048 game by G. Cirulli, scores are given as follows:
%C . combining together two 2^(k-1) tiles, to form a 2^k tile, you get (k-1)*2^k points;
%C . nine times out of ten you get a [2] new tile on the board, while, one time out of ten, appears a [4] tile.
%H Marco Ripà, <a href="http://www.matematicamente.it/giochi-gare/103-gioca-con-la-matematica/11173-2048-gane-massimo-punteggio">2048 game: massimo punteggio</a>, matematicamente.it, June 2014 (in Italian).
%F a(n) = 4*(n^2-1)*(2^n^2-1).
%e For n=4, the maximum score you can achieve with a perfect game is a(4)=3932100. You can get it less than one out of 10^6011 (perfect) games played.
%t A244056[n_] := 4*(n^2-1)*(2^n^2-1);
%t Array[A244056, 15] (* _Paolo Xausa_, Jan 31 2024 *)
%K nonn,easy
%O 1,2
%A _Marco Ripà_, Jun 18 2014
%E a(12) corrected by _Colin Barker_, Jun 18 2014
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