

A060870


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


2



4, 144, 3844, 97344, 2439844, 61027344, 1525839844, 38146777344, 953673339844, 23841853027344, 596046423339844, 14901161071777344, 372529029235839844, 9313225743103027344, 232830643638610839844, 5820766091270446777344
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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) / ((x1)*(5*x1)*(25*x1)). [Colin Barker, Dec 23 2012]


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^n1)^2/4, {n, 20}] (* or *) LinearRecurrence[{31, 155, 125}, {4, 144, 3844}, 20] (* Harvey P. Dale, Dec 06 2014 *)


PROG

(PARI) { for (n=1, 200, write("b060870.txt", 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)mydeja.com), May 04 2001


EXTENSIONS

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


STATUS

approved



