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A060870
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Number of n X n matrices over GF(5) with rank 1.
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2
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4, 144, 3844, 97344, 2439844, 61027344, 1525839844, 38146777344, 953673339844, 23841853027344, 596046423339844, 14901161071777344, 372529029235839844, 9313225743103027344, 232830643638610839844, 5820766091270446777344
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 1/4 * (5^n - 1)^2.
G.f.: -4*x*(5*x+1) / ((x-1)*(5*x-1)*(25*x-1)). [Colin Barker, Dec 23 2012]
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EXAMPLE
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a(2) = 144 because there are 145 (the second element in sequence A060720) singular 2 X 2 matrices over GF(5), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 145 - 1 = 144.
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MATHEMATICA
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Table[(5^n-1)^2/4, {n, 20}] (* or *) LinearRecurrence[{31, -155, 125}, {4, 144, 3844}, 20] (* Harvey P. Dale, Dec 06 2014 *)
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PROG
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(PARI) { for (n=1, 200, write("b060870.txt", n, " ", (5^n - 1)^2 / 4); ) } \\ Harry J. Smith, Jul 13 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001
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STATUS
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approved
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