A060870 Number of n X n matrices over GF(5) with rank 1.

4, 144, 3844, 97344, 2439844, 61027344, 1525839844, 38146777344, 953673339844, 23841853027344, 596046423339844, 14901161071777344, 372529029235839844, 9313225743103027344, 232830643638610839844, 5820766091270446777344, 145519152283287048339844, 3637978807089805603027344

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

Keywords

• nonn
• easy

Examples

			a(2) = 144 because there are 145 (the second element in sequence A060720) singular 2 X 2 matrices over GF(5), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 145 - 1 = 144.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (31,-155,125).

Crossrefs

Cf. A060720.

Programs

Mathematica

Table[(5^n-1)^2/4,{n,20}] (* or *) LinearRecurrence[{31,-155,125},{4,144,3844},20] (* Harvey P. Dale, Dec 06 2014 *)

PARI

a(n) = { (5^n - 1)^2 / 4 } \\ Harry J. Smith, Jul 13 2009

Formula

a(n) = 1/4 * (5^n - 1)^2.

G.f.: -4*x*(5*x+1) / ((x-1)*(5*x-1)*(25*x-1)). [Colin Barker, Dec 23 2012]

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001