A052498 Number of nonsingular n X n matrices over GF(11).

1, 10, 13200, 2124276000, 41393302251840000, 97602635428252959312000000, 27847155251069188894843979022720000000, 961359275427083998992553051820498439890246400000000

Offset: 0

Author

Vladeta Jovovic, Mar 16 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A027879, A110195.

Cf. A002884, A053290, A053291, A053292, A053293, A052496, A052497, A132267.

Programs

Magma

[1] cat [&*[(11^n - 11^k): k in [0..n-1]]: n in [1..10]]; // Bruno Berselli, Jan 28 2013

Mathematica

Table[Product[11^n - 11^k, {k, 0, n-1}], {n, 0, 10}] (* Vincenzo Librandi, Jan 28 2013 *)

PARI

{a(n) = prod(j=0,n-1, 11^n - 11^j)}; \\ G. C. Greubel, May 14 2019

Sage

[product(11^n - 11^j for j in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 14 2019

Formula

a(n) = (11^n - 1)*(11^n - 11)*...*(11^n - 11^(n-1)).

a(n) = A110195(n)*A027879(n). - Bruno Berselli, Jan 30 2013

a(n) ~ c * 11^(n^2), where c = A132267. - Amiram Eldar, Jul 06 2025