A060868 Number of n X n matrices over GF(3) with rank 1.

2, 32, 338, 3200, 29282, 264992, 2389298, 21516800, 193690562, 1743333152, 15690352658, 141214236800, 1270931319842, 11438391444512, 102945551698418, 926510051379200, 8338590720693122, 75047317261079072, 675425857674234578, 6078832726041680000, 54709494555295826402

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Column k=3 of A379587.

Cf. A060705, A060867, A060869, A238976.

Programs

PARI

a(n) = { (3^n - 1)^2 / 2 } \\ Harry J. Smith, Jul 13 2009

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

E.g.f.: exp(x)*(1 - 2*exp(2*x) + exp(8*x))/2. - Stefano Spezia, Dec 26 2024

Extensions

More terms from Jason Earls, May 05 2001