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A224337
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Number of idempotent 6X6 0..n matrices of rank 5.
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1
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378, 2910, 12282, 37494, 93306, 201678, 393210, 708582, 1199994, 1932606, 2985978, 4455510, 6453882, 9112494, 12582906, 17038278, 22674810, 29713182, 38399994, 49009206, 61843578, 77236110, 95551482, 117187494, 142576506, 172186878
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 12*n^5 + 60*n^4 + 120*n^3 + 120*n^2 + 60*n + 6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Colin Barker, Sep 20 2014
G.f.: -6*x*(x^5-7*x^4+18*x^3-82*x^2-107*x-63) / (x-1)^6. - Colin Barker, Sep 20 2014
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EXAMPLE
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Some solutions for n=3
..1..0..0..0..0..0....1..0..0..0..0..0....1..0..1..0..0..0....1..0..0..0..2..0
..3..0..0..2..2..1....0..1..0..0..2..0....0..1..0..0..0..0....0..1..0..0..1..0
..0..0..1..0..0..0....0..0..1..0..2..0....0..0..0..0..0..0....0..0..1..0..1..0
..0..0..0..1..0..0....0..0..0..1..0..0....0..0..1..1..0..0....0..0..0..1..2..0
..0..0..0..0..1..0....0..0..0..0..0..0....0..0..3..0..1..0....0..0..0..0..0..0
..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..2..1
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PROG
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(PARI) Vec(-6*x*(x^5-7*x^4+18*x^3-82*x^2-107*x-63)/(x-1)^6 + O(x^100)) \\ Colin Barker, Sep 20 2014
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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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STATUS
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approved
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