A244056 Maximum score achievable in the 2048 game on an n X n grid.

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

Table of n, a(n) for n=1..12.

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

Adjacent sequences: A244053 A244054 A244055 * A244057 A244058 A244059

Keyword

nonn,easy

Author

Marco Ripà, Jun 18 2014

Extensions

a(12) corrected by Colin Barker, Jun 18 2014

Status

approved