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A224336
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Number of idempotent 5X5 0..n matrices of rank 4.
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1
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155, 805, 2555, 6245, 12955, 24005, 40955, 65605, 99995, 146405, 207355, 285605, 384155, 506245, 655355, 835205, 1049755, 1303205, 1599995, 1944805, 2342555, 2798405, 3317755, 3906245, 4569755, 5314405, 6146555, 7072805, 8099995, 9235205
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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) = 10*n^4 + 40*n^3 + 60*n^2 + 40*n + 5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Colin Barker, Sep 20 2014
G.f.: -5*x*(x^4-6*x^3+16*x^2+6*x+31) / (x-1)^5. - Colin Barker, Sep 20 2014
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EXAMPLE
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Some solutions for n=3
..1..0..0..1..0....0..0..0..0..0....0..2..3..2..2....1..0..0..1..0
..0..1..0..1..0....1..1..0..0..0....0..1..0..0..0....0..1..0..2..0
..0..0..1..2..0....3..0..1..0..0....0..0..1..0..0....0..0..1..2..0
..0..0..0..0..0....2..0..0..1..0....0..0..0..1..0....0..0..0..0..0
..0..0..0..2..1....3..0..0..0..1....0..0..0..0..1....0..0..0..1..1
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PROG
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(PARI) Vec(-5*x*(x^4-6*x^3+16*x^2+6*x+31)/(x-1)^5 + 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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