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

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

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

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.

Prog

(PARI) { for (n=1, 200, write("b060871.txt", 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