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A224338
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Number of idempotent 7 X 7 0..n matrices of rank 6.
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1
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889, 10199, 57337, 218743, 653177, 1647079, 3670009, 7440167, 13999993, 24801847, 41803769, 67575319, 105413497, 159468743, 234881017, 337925959, 476171129, 658642327, 895999993, 1200725687, 1587318649, 2072502439, 2675441657
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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) = 14*n^6 + 84*n^5 + 210*n^4 + 280*n^3 + 210*n^2 + 84*n + 7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Colin Barker, Sep 20 2014
G.f.: -7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127) / (x-1)^7. - Colin Barker, Sep 20 2014
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EXAMPLE
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Some solutions for n=1
..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..0..0..1..0..0..0
..0..1..0..0..0..0..0....0..1..0..0..0..1..0....0..1..0..0..0..0..0
..0..0..1..0..0..0..0....0..0..1..0..0..1..0....0..0..1..0..0..0..0
..0..0..0..0..0..1..1....0..0..0..1..0..0..0....0..0..0..0..0..0..0
..0..0..0..0..1..0..0....0..0..0..0..1..1..0....0..0..0..1..1..0..0
..0..0..0..0..0..1..0....0..0..0..0..0..0..0....0..0..0..0..0..1..0
..0..0..0..0..0..0..1....0..0..0..0..0..1..1....0..0..0..1..0..0..1
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PROG
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(PARI) Vec(-7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127)/(x-1)^7 + 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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