A060871 Number of n X n matrices over GF(7) with rank 1.

6, 384, 19494, 960000, 47073606, 2306841984, 113036904294, 5538819840000, 271402252867206, 13298710955443584, 651636840771389094, 31930205225480640000, 1564580056242329380806, 76664422757230585805184, 3756556715113793827473894, 184071279040642363407360000

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 (57,-399,343).

Formula

a(n) = (7^n - 1)^2/6.

G.f.: -6*x*(7*x+1)/((x-1)*(7*x-1)*(49*x-1)). - Colin Barker, Dec 23 2012

From Elmo R. Oliveira, Dec 09 2025: (Start)

E.g.f.: exp(x)*(1 - 2*exp(6*x) + exp(48*x))/6.

a(n) = 57*a(n-1) - 399*a(n-2) + 343*a(n-3) for n > 3. (End)

Example

a(2) = 384 because there are 385 (the second element in sequence A060721) singular 2 X 2 matrices over GF(7), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 385 - 1 = 384.

Mathematica

(7^Range[20] - 1)^2/6 (* Paolo Xausa, May 20 2026 *)

Prog

(PARI) a(n) = { (7^n - 1)^2 / 6 } \\ Harry J. Smith, Jul 13 2009

Crossrefs

Cf. A060721.

Sequence in context: A245398 A078207 A261296 * A370845 A193133 A162137

Adjacent sequences: A060868 A060869 A060870 * A060872 A060873 A060874

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved