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%I #13 Jun 17 2017 03:06:28
%S 155,805,2555,6245,12955,24005,40955,65605,99995,146405,207355,285605,
%T 384155,506245,655355,835205,1049755,1303205,1599995,1944805,2342555,
%U 2798405,3317755,3906245,4569755,5314405,6146555,7072805,8099995,9235205
%N Number of idempotent 5X5 0..n matrices of rank 4.
%C Row 5 of A224333.
%H R. H. Hardin, <a href="/A224336/b224336.txt">Table of n, a(n) for n = 1..210</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 10*n^4 + 40*n^3 + 60*n^2 + 40*n + 5.
%F 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
%F G.f.: -5*x*(x^4-6*x^3+16*x^2+6*x+31) / (x-1)^5. - _Colin Barker_, Sep 20 2014
%e Some solutions for n=3
%e ..1..0..0..1..0....0..0..0..0..0....0..2..3..2..2....1..0..0..1..0
%e ..0..1..0..1..0....1..1..0..0..0....0..1..0..0..0....0..1..0..2..0
%e ..0..0..1..2..0....3..0..1..0..0....0..0..1..0..0....0..0..1..2..0
%e ..0..0..0..0..0....2..0..0..1..0....0..0..0..1..0....0..0..0..0..0
%e ..0..0..0..2..1....3..0..0..0..1....0..0..0..0..1....0..0..0..1..1
%o (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
%K nonn,easy
%O 1,1
%A _R. H. Hardin_, formula via _M. F. Hasler_ _William J. Keith_ and _Rob Pratt_ in the Sequence Fans Mailing List, Apr 03 2013
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