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Number of nonsingular n X n matrices over GF(7).
14

%I #28 Sep 13 2023 11:08:22

%S 1,6,2016,33784128,27811094169600,1122211189922928537600,

%T 2218959336124989671614429593600,

%U 214992513152176999576908105619651923148800,1020690003311610463765638355505358381593396977336320000,237443634207909205360438080389756681126654524500073656592021585920000

%N Number of nonsingular n X n matrices over GF(7).

%H Vincenzo Librandi, <a href="/A053293/b053293.txt">Table of n, a(n) for n = 0..30</a>

%H J. Overbey, W. Traves and J. Wojdylo, <a href="http://jeff.over.bz/papers/undergrad/on-the-keyspace-of-the-hill-cipher.pdf">On the Keyspace of the Hill Cipher</a>.

%F a(n) = (7^n - 1)*(7^n - 7)*...*(7^n - 7^(n-1)).

%F a(n) = A109493(n)*A027875(n). - _Bruno Berselli_, Jan 30 2013

%t Table[Product[7^n - 7^k, {k, 0, n-1}], {n, 0, 10}] (* _Vincenzo Librandi_, Jan 28 2013 *)

%o (Magma) [1] cat [&*[(7^n - 7^k): k in [0..n-1]]: n in [1..7]]; // _Bruno Berselli_, Jan 28 2013

%o (PARI) for(n=0,10, print1(prod(k=0,n-1, 7^n - 7^k), ", ")) \\ _G. C. Greubel_, May 31 2018

%Y Column k=7 of A316622.

%Y Cf. A002884, A003790, A027875, A053290-A053292, A109493.

%K nonn,easy

%O 0,2

%A _Stephen G Penrice_, Mar 04 2000

%E More terms from _Vladeta Jovovic_, Mar 16 2000