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a(n) = 2^(n^2-1).
10

%I #24 Jul 05 2024 11:23:27

%S 1,8,256,32768,16777216,34359738368,281474976710656,

%T 9223372036854775808,1208925819614629174706176,

%U 633825300114114700748351602688,1329227995784915872903807060280344576,11150372599265311570767859136324180752990208

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

%C From the classic story: number of grains of wheat on last square of n X n chessboard.

%C Hankel transform of A059304 and of A084771. - _Philippe Deléham_, Dec 02 2007

%C The number of compositions of n^2. - _Alois P. Heinz_, Feb 22 2020

%H Vincenzo Librandi, <a href="/A103488/b103488.txt">Table of n, a(n) for n = 1..50</a>

%H Peter Kagey and William Keehn, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Kagey/kagey6.html">Counting Tilings of the n X m Grid, Cylinder, and Torus</a>, J. Int. Seq. (2024) Vol. 27, Art. No. 24.6.1. See section A, pp. 6, 10.

%F a(n) = A000079(A005563(n-1)). - _Michel Marcus_, Feb 25 2014

%F a(n) = A011782(A000290(n)). - _Alois P. Heinz_, Feb 22 2020

%p [seq(2^(n^2-1),n=1..14)];

%t Table[2^(n^2 - 1), {n, 1, 20}] (* _Vincenzo Librandi_, Feb 25 2014 *)

%o (PARI) a(n) = 2^(n^2-1); \\ _Joerg Arndt_, Feb 23 2014

%o (Magma) [2^(n^2-1): n in [1..15]]; // _Vincenzo Librandi_, Feb 25 2014

%Y Cf. A000079, A000290, A005563, A011782.

%K easy,nonn

%O 1,2

%A _Zerinvary Lajos_, Jul 30 2006