A065498 Number of invertible n X n matrices mod 6 (i.e., over the ring Z_6).

1, 2, 288, 1886976, 489104179200, 4755360379856486400, 1695944421638473850132889600, 21967113634648374162210646578639667200, 10286692771039109536373764545035369981946101760000, 173770439600109774111384717714984362383506603790098046648320000

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.

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.

Formula

a(n) = 6^(n^2) * Product_{k=1..n} ((1 - 1/2^k)(1 - 1/3^k)).

a(n) = A002884(n)*A053290(n). - Geoffrey Critzer, Jan 26 2018

a(n) ~ c * 6^(n^2), where c = A048651 * A100220 = 0.161757743053... . - Amiram Eldar, Jul 06 2025

Mathematica

a[n_] := 6^(n^2)*Product[(1 - 1/2^k)*(1 - 1/3^k), { k, 1, n} ]; Table[ a[n], {n, 0, 9} ]

Crossrefs

Column k=6 of A316622.

Cf. A002884, A048651, A053290, A065128, A100220.

Sequence in context: A279450 A357733 A163276 * A296591 A296607 A203771

Adjacent sequences: A065495 A065496 A065497 * A065499 A065500 A065501

Keyword

nonn,easy

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Nov 25 2001

Extensions

More terms from Robert G. Wilson v, Nov 28 2001

Status

approved