A086752 Number of n X n matrices over GF(3) with rank n-1.

1, 32, 8112, 17971200, 355207057920, 63010655570903040, 100505356319291594711040, 1442361950110091891786121216000, 186276322602412236974585775503690956800, 216505458700483736766078241517019274701019545600, 2264736353104098912130003755084217747715114856943819161600

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 31 2003

Keywords

• nonn
• easy

Crossrefs

Cf. A086699, A053290, A060868.

Programs

Mathematica

Table[3^(n^2) * (1 - 1/3^n) * QPochhammer[1/3^n, 3, n-1]/2, {n, 1, 10}] (* Vaclav Kotesovec, Apr 14 2024 *)

Formula

For n>=2: a(n) = Product_{j=0..n-2} (3^n - 3^j)^2 / (3^(n-1)- 3^j).

a(n) = ((3^n-1)/2)*Product_{j=0..n-2} (3^n-3^j). - David Wasserman, Mar 28 2005

Extensions

More terms from David Wasserman, Mar 28 2005