A069580 Number of noninvertible n X n matrices mod 4 (i.e., over the ring Z_4).

2, 160, 176128, 2973761536, 790377061679104, 3337070496489549070336, 224673304169436873829314985984, 241628003280411784073600553618302304256, 4154447778684876644944282114016459737751307157504, 1142419984262996237357582885893433282120743128964441021874176

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), Apr 18 2002

Keywords

• nonn

Crossrefs

Cf. A011787, A048651, A065128.

Programs

Mathematica

a[n_] := 4^(n^2) * (1 - Product[1 - 1/2^k, {k, 1, n}]); Array[a, 10] (* Amiram Eldar, Jul 12 2025 *)

PARI

a(n) = 4^(n^2) * (1 - prod(k = 1, n, 1-1/2^k)); \\ Amiram Eldar, Jul 12 2025

Formula

a(n) = 4^(n^2) - A065128(n).

a(n) ~ c * 4^(n^2), where c = 1 - A048651. - Amiram Eldar, Jul 12 2025

Extensions

More terms from Max Alekseyev, Jan 23 2012