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

1,1

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).

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

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

Crossrefs

Column k=3 of A379587.

Cf. A060705, A060867, A060869, A238976.

Sequence in context: A053065 A091707 A323639 * A350138 A270445 A199019

Adjacent sequences: A060865 A060866 A060867 * A060869 A060870 A060871

Keyword

nonn,easy,changed

Author

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

Extensions

More terms from Jason Earls, May 05 2001

Status

approved