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
Links
- 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.
Programs
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Mathematica
a[n_] := 4^(n^2)*Product[1 - 1/2^k, {k, 1, n} ]; Table[ a[n], {n, 0, 10} ] -
PARI
for(n=1,11,print(4^(n^2)*prod(k=1,n,(1-1/2^k))))
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
From Amiram Eldar, Jul 06 2025: (Start)
a(n) = Product_{k=1..n} 2*A060195(k).
a(n) ~ c * 4^(n^2), where c = A048651. (End)
Extensions
More terms from Robert G. Wilson v and Jason Earls, Nov 16 2001