A053290 Number of nonsingular n X n matrices over GF(3).

1, 2, 48, 11232, 24261120, 475566474240, 84129611558952960, 134068444202678083338240, 1923442429811445711790394572800, 248381049201184165590947520186915225600, 288678833735376059528974260112416365258106470400

Offset: 0

Author

Stephen G Penrice, Mar 04 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..45
• 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=3 of A316622.

Cf. A002884, A003787, A027871, A047656, A053291, A053292, A053293.

Cf. A100220, A219205.

Programs

Magma

[1] cat [&*[(3^n - 3^k): k in [0..n-1]]: n in [1..9]]; // Bruno Berselli, Jan 28 2013

Mathematica

Table[Product[3^n - 3^k, {k, 0, n - 1}], {n, 0, 10}] (* Geoffrey Critzer, Jan 26 2013; edited by Vincenzo Librandi, Jan 28 2013 *)

PARI

for(n=0,10, print1(prod(k=0,n-1, 3^n - 3^k), ", ")) \\ G. C. Greubel, May 31 2018

Formula

a(n) = Product_{k=0..n-1}(3^n-3^k). - corrected by Michel Marcus, Sep 18 2015

a(n) = A047656(n)*A027871(n). - Bruno Berselli, Jan 30 2013

From Amiram Eldar, Jul 06 2025: (Start)

a(n) = Product_{k=1..n} A219205(k).

a(n) ~ c * 3^(n^2), where c = A100220. (End)

Extensions

More terms from Vladeta Jovovic, Mar 16 2000