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A060871 Number of n X n matrices over GF(7) with rank 1. 1
6, 384, 19494, 960000, 47073606, 2306841984, 113036904294, 5538819840000, 271402252867206, 13298710955443584, 651636840771389094, 31930205225480640000, 1564580056242329380806, 76664422757230585805184 (list; graph; refs; listen; history; text; internal format)
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 * A193133 A162137 A119645

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

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)