%I #30 Dec 26 2024 16:57:58
%S 2,32,338,3200,29282,264992,2389298,21516800,193690562,1743333152,
%T 15690352658,141214236800,1270931319842,11438391444512,
%U 102945551698418,926510051379200,8338590720693122,75047317261079072,675425857674234578,6078832726041680000,54709494555295826402
%N Number of n X n matrices over GF(3) with rank 1.
%H Harry J. Smith, <a href="/A060868/b060868.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 (13,-39,27).
%F a(n) = 1/2 * (3^n - 1)^2.
%F G.f.: -2*x*(3*x+1) / ((x-1)*(3*x-1)*(9*x-1)). - _Colin Barker_, Dec 23 2012
%F E.g.f.: exp(x)*(1 - 2*exp(2*x) + exp(8*x))/2. - _Stefano Spezia_, Dec 26 2024
%e a(2) = 32 because there are 33 (the second element in sequence A060705) singular 2 X 2 matrices over GF(3), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 33 - 1 = 32.
%o (PARI) a(n) = { (3^n - 1)^2 / 2 } \\ _Harry J. Smith_, Jul 13 2009
%Y Column k=3 of A379587.
%Y Cf. A060705, A060867, A060869, A238976.
%K nonn,easy
%O 1,1
%A Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001
%E More terms from _Jason Earls_, May 05 2001