A065128 Number of invertible n X n matrices mod 4 (i.e., over the ring Z_4).

1, 2, 96, 86016, 1321205760, 335522845163520, 1385295986380096143360, 92239345887620476544860815360, 98654363640526679389774053813465907200, 1691558770638735027870457216848672340872423014400, 464518059995994038184379206447729320401459864818351813427200

Offset

0,2

Links

Table of n, a(n) for n=0..10.

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

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

Formula

a(n) = 4^(n^2) * Product_{k=1..n} (1 - 1/2^k).

a(n) = 2^(n^2) * A002884(n). - Geoffrey Critzer, Feb 04 2018

Mathematica

a(0) = 1. a[n_] := 4^(n^2)*Product[1 - 1/2^k, {k, 1, n} ]; Table[ a[n], {n, 0, 10} ]

Prog

(PARI) for(n=1, 11, print(4^(n^2)*prod(k=1, n, (1-1/2^k))))

Crossrefs

Column k=4 of A316622.

Cf. A053291.

Sequence in context: A119696 A264542 A064069 * A122222 A036980 A337653

Adjacent sequences: A065125 A065126 A065127 * A065129 A065130 A065131

Keyword

nonn

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Nov 14 2001

Extensions

More terms from Robert G. Wilson v and Jason Earls, Nov 16 2001

Status

approved