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A060868
Number of n X n matrices over GF(3) with rank 1.
2
2, 32, 338, 3200, 29282, 264992, 2389298, 21516800, 193690562, 1743333152, 15690352658, 141214236800, 1270931319842, 11438391444512, 102945551698418, 926510051379200, 8338590720693122, 75047317261079072, 675425857674234578
OFFSET
1,1
FORMULA
a(n) = 1/2 * (3^n - 1)^2.
G.f.: -2*x*(3*x+1) / ((x-1)*(3*x-1)*(9*x-1)). [Colin Barker, Dec 23 2012]
EXAMPLE
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.
PROG
(PARI) { for (n=1, 200, write("b060868.txt", n, " ", (3^n - 1)^2 / 2); ) } \\ Harry J. Smith, Jul 13 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001
EXTENSIONS
More terms from Jason Earls, May 05 2001
STATUS
approved