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

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

Offset

0,2

Links

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

J. Overbey, W. Traves and J. Wojdylo, On the Keyspace of the Hill Cipher.

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

Mathematica

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

Prog

(Magma) [1] cat [&*[(5^n - 5^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013
(PARI) for(n=0, 10, print1(prod(k=0, n-1, 5^n - 5^k), ", ")) \\ G. C. Greubel, May 31 2018

Crossrefs

Column k=5 of A316622.

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

Sequence in context: A215220 A035483 A145570 * A053963 A053941 A027678

Adjacent sequences: A053289 A053290 A053291 * A053293 A053294 A053295

Keyword

nonn,easy

Author

Stephen G Penrice, Mar 04 2000

Extensions

More terms from Vladeta Jovovic, Mar 16 2000

Status

approved