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A224337 Number of idempotent 6X6 0..n matrices of rank 5.

%I A224337 #13 Jun 17 2017 03:53:57
%S A224337 378,2910,12282,37494,93306,201678,393210,708582,1199994,1932606,
%T A224337 2985978,4455510,6453882,9112494,12582906,17038278,22674810,29713182,
%U A224337 38399994,49009206,61843578,77236110,95551482,117187494,142576506,172186878
%N A224337 Number of idempotent 6X6 0..n matrices of rank 5.
%C A224337 Row 6 of A224333.
%H A224337 R. H. Hardin, <a href="/A224337/b224337.txt">Table of n, a(n) for n = 1..210</a>
%H A224337 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A224337 a(n) = 12*n^5 + 60*n^4 + 120*n^3 + 120*n^2 + 60*n + 6.
%F A224337 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
%F A224337 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
%e A224337 Some solutions for n=3
%e A224337 ..1..0..0..0..0..0....1..0..0..0..0..0....1..0..1..0..0..0....1..0..0..0..2..0
%e A224337 ..3..0..0..2..2..1....0..1..0..0..2..0....0..1..0..0..0..0....0..1..0..0..1..0
%e A224337 ..0..0..1..0..0..0....0..0..1..0..2..0....0..0..0..0..0..0....0..0..1..0..1..0
%e A224337 ..0..0..0..1..0..0....0..0..0..1..0..0....0..0..1..1..0..0....0..0..0..1..2..0
%e A224337 ..0..0..0..0..1..0....0..0..0..0..0..0....0..0..3..0..1..0....0..0..0..0..0..0
%e A224337 ..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..2..1
%o A224337 (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
%K A224337 nonn,easy
%O A224337 1,1
%A A224337 _R. H. Hardin_, formula via _M. F. Hasler_ _William J. Keith_ and _Rob Pratt_ in the Sequence Fans Mailing List, Apr 03 2013