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%I #15 Jan 12 2017 01:53:50
%S 6,384,19494,960000,47073606,2306841984,113036904294,5538819840000,
%T 271402252867206,13298710955443584,651636840771389094,
%U 31930205225480640000,1564580056242329380806,76664422757230585805184
%N Number of n X n matrices over GF(7) with rank 1.
%H Harry J. Smith, <a href="/A060871/b060871.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 (57,-399,343).
%F a(n) = 1/6 * (7^n - 1)^2.
%F G.f.: -6*x*(7*x+1) / ((x-1)*(7*x-1)*(49*x-1)). [_Colin Barker_, Dec 23 2012]
%e a(2) = 384 because there are 385 (the second element in sequence A060721) singular 2 X 2 matrices over GF(7), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 385 - 1 = 384.
%o (PARI) { for (n=1, 200, write("b060871.txt", n, " ", (7^n - 1)^2 / 6); ) } \\ _Harry J. Smith_, Jul 13 2009
%Y Cf. A060721.
%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), May 07 2001
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