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Number of n X n matrices over GF(4) with rank 1.
4

%I #19 Dec 15 2017 17:35:00

%S 3,75,1323,21675,348843,5589675,89467563,1431612075,22906317483,

%T 366503176875,5864059218603,93824981052075,1501199831050923,

%U 24019197833685675,384307167486454443,6148914688373205675,98382635048331029163,1574122160910735420075

%N Number of n X n matrices over GF(4) with rank 1.

%H Harry J. Smith, <a href="/A060869/b060869.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).

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

%F G.f.: -3*x*(4*x+1) / ((x-1)*(4*x-1)*(16*x-1)). [_Colin Barker_, Dec 23 2012]

%e 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.

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

%Y A060716.

%K nonn,easy

%O 1,1

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

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, May 07 2001

%E More terms from _Colin Barker_, Dec 23 2012