A060869 Number of n X n matrices over GF(4) with rank 1.

3, 75, 1323, 21675, 348843, 5589675, 89467563, 1431612075, 22906317483, 366503176875, 5864059218603, 93824981052075, 1501199831050923, 24019197833685675, 384307167486454443, 6148914688373205675, 98382635048331029163, 1574122160910735420075

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 (21,-84,64).

Formula

a(n) = 1/3 * (4^n - 1)^2.

G.f.: -3*x*(4*x+1) / ((x-1)*(4*x-1)*(16*x-1)). [Colin Barker, Dec 23 2012]

Example

a(2) = 75 because there are 76 (the second element in sequence A060716) singular 2 X 2 matrices over GF(4), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 76 - 1 = 75.

Prog

(PARI) { for (n=1, 200, write("b060869.txt", n, " ", (4^n - 1)^2 / 3); ) } \\ Harry J. Smith, Jul 13 2009

Crossrefs

A060716.

Sequence in context: A343808 A125520 A163131 * A012491 A136328 A003690

Adjacent sequences: A060866 A060867 A060868 * A060870 A060871 A060872

Keyword

nonn,easy

Author

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, May 07 2001

More terms from Colin Barker, Dec 23 2012

Status

approved