[go: up one dir, main page]

login
A244056
Maximum score achievable in the 2048 game on an n X n grid.
1
0, 180, 16352, 3932100, 3221225376, 9620726742900, 108086391056891712, 4648579506574807006980, 773712524553362671811952320, 501989637690378842992694469328500, 1276058875953519237987654777869130792480, 12756026253559516436958430851954862781420797380
OFFSET
1,2
COMMENTS
This sequence is based on the original 2048 game by G. Cirulli, scores are given as follows:
. combining together two 2^(k-1) tiles, to form a 2^k tile, you get (k-1)*2^k points;
. nine times out of ten you get a [2] new tile on the board, while, one time out of ten, appears a [4] tile.
LINKS
Marco Ripà, 2048 game: massimo punteggio, matematicamente.it, June 2014 (in Italian).
FORMULA
a(n) = 4*(n^2-1)*(2^n^2-1).
EXAMPLE
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.
MATHEMATICA
A244056[n_] := 4*(n^2-1)*(2^n^2-1);
Array[A244056, 15] (* Paolo Xausa, Jan 31 2024 *)
CROSSREFS
Sequence in context: A287022 A217791 A035830 * A091033 A146530 A057867
KEYWORD
nonn,easy
AUTHOR
Marco Ripà, Jun 18 2014
EXTENSIONS
a(12) corrected by Colin Barker, Jun 18 2014
STATUS
approved