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a(n) = 2^(n^2) - 1.
1

%I #27 Sep 30 2024 14:22:01

%S 0,1,15,511,65535,33554431,68719476735,562949953421311,

%T 18446744073709551615,2417851639229258349412351,

%U 1267650600228229401496703205375,2658455991569831745807614120560689151,22300745198530623141535718272648361505980415

%N a(n) = 2^(n^2) - 1.

%C Number of grains for squared chessboards.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem">Wheat and chessboard problem</a>

%F a(n) = 2^(n^2) - 1 = A002416(n) - 1. - _Omar E. Pol_, Jun 11 2012

%e For usual 8 X 8 chessboard there are 2^64 - 1 = 18446744073709551615 grains.

%p a:= n-> 2^(n^2)-1:

%p seq(a(n), n=0..15);

%t 2^Range[0, 12]^2 - 1 (* _Paul F. Marrero Romero_, Sep 30 2024 *)

%Y Cf. A000225, A002416.

%K nonn

%O 0,3

%A _Jani Melik_, Jun 06 2012

%E Better name from _Omar E. Pol_, Jun 11 2012