A069920 Number of noninvertible n X n matrices mod 6 (i.e., over the ring Z_6).

4, 1008, 8190720, 2332005728256, 23674927650073214976, 8618480376852061696039059456, 112746432609478969278312620164116381696, 53053593891934168169788522401776516627950360068096, 898369021875992553077210146021642426986208034219512412195782656

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 05 2002

Keywords

• nonn

Crossrefs

Cf. A048651, A065498, A069580, A100220 .

Programs

Mathematica

a[n_] := 6^(n^2) * (1 - Product[(1 - 1/2^k) * (1 - 1/3^k), {k, 1, n}]); Array[a, 10] (* Amiram Eldar, Jul 12 2025 *)

PARI

a(n) = 6^(n^2)*(1-prod(k=1,n,(1-1/2^k)*(1-1/3^k)));

Formula

a(n) = 6^(n^2) - A065498(n).

a(n) ~ c * 6^(n^2), where c = 1 - A048651 * A100220 = 0.838242256946... . - Amiram Eldar, Jul 12 2025

Extensions

More terms from Benoit Cloitre, May 11 2002