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, 25185954575121522535083
Offset: 1
Examples
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.
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).
Programs
-
PARI
a(n) = { (4^n - 1)^2 / 3 } \\ Harry J. Smith, Jul 13 2009
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
E.g.f.: exp(x)*(1 - 2*exp(3*x) + exp(15*x))/3. - Stefano Spezia, Dec 26 2024
Extensions
More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, May 07 2001
More terms from Colin Barker, Dec 23 2012