A053293 Number of nonsingular n X n matrices over GF(7).

1, 6, 2016, 33784128, 27811094169600, 1122211189922928537600, 2218959336124989671614429593600, 214992513152176999576908105619651923148800, 1020690003311610463765638355505358381593396977336320000, 237443634207909205360438080389756681126654524500073656592021585920000

Offset: 0

Author

Stephen G Penrice, Mar 04 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..30
• Jeffrey Overbey, William Traves, and Jerzy Wojdylo, On the Keyspace of the Hill Cipher, Cryptologia, Vol. 29, Iss. 1 (2005), pp. 59-72; author's copy.

Crossrefs

Column k=7 of A316622.

Cf. A002884, A003790, A027875, A053290, A053291, A053292, A109493, A132035.

Programs

Magma

[1] cat [&*[(7^n - 7^k): k in [0..n-1]]: n in [1..7]]; // Bruno Berselli, Jan 28 2013

Mathematica

Table[Product[7^n - 7^k, {k, 0, n-1}], {n, 0, 10}] (* Vincenzo Librandi, Jan 28 2013 *)

PARI

for(n=0,10, print1(prod(k=0,n-1, 7^n - 7^k), ", ")) \\ G. C. Greubel, May 31 2018

Formula

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

a(n) = A109493(n)*A027875(n). - Bruno Berselli, Jan 30 2013

a(n) ~ c * 7^(n^2), where c = A132035. - Amiram Eldar, Jul 06 2025

Extensions

More terms from Vladeta Jovovic, Mar 16 2000