A051680 Number of n X n invertible matrices A over GF(3) such that A-I is invertible.

1, 27, 6291, 13589289, 266377183929, 47123189360124723, 75095231825148137471259, 1077370264330489309698453375441, 139124702920688202983704723564457669361

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Formula

a(n) = 3^binomial(n,2)*b(n), with b(0)=1, b(n)=(3^n-1)*b(n-1)+(-1)^(n). - Vladeta Jovovic, Aug 20 2006

From Geoffrey Critzer, Oct 17 2021: (Start)

Sum_{n>=0} a(n)*u^n/A053290(n) = 1/(1-u)*Product_{r>=1} 1-u/3^r.

Limit_{n->inf} a(n)/3^(n^2) = (Product_{r>=1} 1-1/3^r)^2. (End)

Mathematica

a[n_] := a[n] = 3^(n-1)*((3^n-1)*a[n-1] + (-1)^n*3^((n-3)*n/2+1)); a[1] = 1; Table[a[n], {n, 1, 9}] (* Jean-François Alcover, Jan 12 2012, after formula *)

Crossrefs

Cf. A002820.

Sequence in context: A059795 A211928 A123395 * A013828 A343922 A209261

Adjacent sequences: A051677 A051678 A051679 * A051681 A051682 A051683

Keyword

nonn,nice

Author

Vladeta Jovovic, Mar 17 2000

Status

approved