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A060869 Number of n X n matrices over GF(4) with rank 1. 3
3, 75, 1323, 21675, 348843, 5589675, 89467563, 1431612075, 22906317483, 366503176875, 5864059218603, 93824981052075, 1501199831050923, 24019197833685675, 384307167486454443, 6148914688373205675, 98382635048331029163, 1574122160910735420075 (list; graph; refs; listen; history; text; internal format)
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 (21,-84,64).

FORMULA

a(n) = 1/3 * (4^n - 1)^2.

G.f.: -3*x*(4*x+1) / ((x-1)*(4*x-1)*(16*x-1)). [Colin Barker, Dec 23 2012]

EXAMPLE

a(2) = 75 because there are 76 (the second element in sequence A060716) singular 2 X 2 matrices over GF(4), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 76 - 1 = 75.

PROG

(PARI) { for (n=1, 200, write("b060869.txt", n, " ", (4^n - 1)^2 / 3); ) } \\ Harry J. Smith, Jul 13 2009

CROSSREFS

A060716.

Sequence in context: A230145 A125520 A163131 * A012491 A136328 A003690

Adjacent sequences:  A060866 A060867 A060868 * A060870 A060871 A060872

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

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

More terms from Colin Barker, Dec 23 2012

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)