A053292 Number of nonsingular n X n matrices over GF(5).

1, 4, 480, 1488000, 116064000000, 226614960000000000, 11064475422000000000000000, 13506266841692625000000000000000000, 412177498341354683437500000000000000000000000

Offset: 0

Author

Stephen G Penrice, Mar 04 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..35
• 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=5 of A316622.

Cf. A002884, A003789, A027872, A053290, A053291, A053293, A109345, A100222.

Programs

Magma

[1] cat [&*[(5^n - 5^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013

Mathematica

Table[Product[5^n - 5^k, {k,0,n-1}], {n,0,10}] (* Geoffrey Critzer, Jan 26 2013 *)

PARI

for(n=0,10, print1(prod(k=0,n-1, 5^n - 5^k), ", ")) \\ G. C. Greubel, May 31 2018

Formula

a(n) = (5^n - 1)*(5^n - 5)*...*(5^n - 5^(n-1)).

a(n) = A109345(n)*A027872(n). - Bruno Berselli, Jan 30 2013

a(n) ~ c * 5^(n^2), where c = A100222. - Amiram Eldar, Jul 06 2025

Extensions

More terms from Vladeta Jovovic, Mar 16 2000