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A224337
Number of idempotent 6X6 0..n matrices of rank 5.
1
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
OFFSET
1,1
COMMENTS
Row 6 of A224333.
FORMULA
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
EXAMPLE
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
PROG
(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
CROSSREFS
Sequence in context: A157116 A071624 A058041 * A239174 A235761 A154078
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, formula via M. F. Hasler William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013
STATUS
approved