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

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

Offset

0,2

Links

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

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

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

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 *)

Prog

(Magma) [1] cat [&*[(3^n - 3^k): k in [0..n-1]]: n in [1..9]]; // Bruno Berselli, Jan 28 2013
(PARI) for(n=0, 10, print1(prod(k=0, n-1, 3^n - 3^k), ", ")) \\ G. C. Greubel, May 31 2018

Crossrefs

Column k=3 of A316622.

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

Sequence in context: A238838 A002820 A196448 * A056989 A352207 A230886

Adjacent sequences: A053287 A053288 A053289 * A053291 A053292 A053293

Keyword

nonn,easy

Author

Stephen G Penrice, Mar 04 2000

Extensions

More terms from Vladeta Jovovic, Mar 16 2000

Status

approved