A053291 Nonsingular n X n matrices over GF(4).

1, 3, 180, 181440, 2961100800, 775476766310400, 3251791214634074112000, 218210695042457748180566016000, 234298374547168764346587444978647040000, 4025200069765920285793155323595159699896401920000, 1106437515026051855463365435310419366987397763763798016000000

Offset: 0

Author

Stephen G Penrice, Mar 04 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A002884, A003788, A027637, A053763, A053290, A053292, A053293.

Cf. A100221, A115490.

Programs

Magma

[1] cat [&*[(4^n - 4^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013

Mathematica

Table[Product[4^n - 4^k, {k,0,n-1}], {n,0,10}] (* Geoffrey Critzer, Jan 26 2013 *)

PARI

for(n=0,10, print1(prod(k=0,n-1, 4^n - 4^k), ", ")) \\ G. C. Greubel, May 31 2018

Formula

a(n) = (4^n - 1)*(4^n - 4)*...*(4^n - 4^(n-1)).

a(n) = A053763(n)*A027637(n). - Bruno Berselli, Jan 30 2013

From Amiram Eldar, Jul 06 2025: (Start)

a(n) = Product_{k=1..n} A115490(k).

a(n) ~ c * 4^(n^2), where c = A100221. (End)

Extensions

More terms from Vladeta Jovovic, Mar 16 2000