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

1,1

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).

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

From Elmo R. Oliveira, Dec 09 2025: (Start)

E.g.f.: exp(x)*(1 - 2*exp(4*x) + exp(24*x))/4.

a(n) = 31*a(n-1) - 155*a(n-2) + 125*a(n-3) for n > 3. (End)

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A060720.

Sequence in context: A036511 A263386 A186720 * A268894 A084703 A186418

Adjacent sequences: A060867 A060868 A060869 * A060871 A060872 A060873

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved