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

Author

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

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

Cf. A060721.

Programs

PARI

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

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

Extensions

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