A052496 Number of nonsingular n X n matrices over GF(8).

1, 7, 3528, 115379712, 241909719367680, 32467582052437076213760, 278893342293098904613804037898240, 153323163270070838469523866093442017326530560

Offset: 0

Author

Vladeta Jovovic, Mar 16 2000

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A027876, A109966.

Cf. A002884, A003791, A053290, A053291, A053292, A053293, A052497, A052498, A132036.

Programs

Magma

[1] cat [&*[(8^n-8^k): k in [0..n-1]]: n in [1..10]]; // Bruno Berselli, Jan 30 2013

Mathematica

Table[Product[(8^n - 8^j), {j, 0, n-1}], {n, 0, 10}] (* G. C. Greubel, May 14 2019 *)

PARI

{a(n) = prod(j=0,n-1, 8^n - 8^j)}; \\ G. C. Greubel, May 14 2019

Sage

[product(8^n - 8^j for j in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 14 2019

Formula

a(n) = (8^n - 1)*(8^n - 8)*...*(8^n - 8^(n-1)).

a(n) = A109966(n)*A027876(n). - Bruno Berselli, Jan 30 2013

a(n) ~ c * 8^(n^2), where c = A132036. - Amiram Eldar, Jul 06 2025