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A224334 Number of idempotent 3 X 3 0..n matrices of rank 2.

%I A224334 #9 Feb 23 2018 11:53:27
%S A224334 21,51,93,147,213,291,381,483,597,723,861,1011,1173,1347,1533,1731,
%T A224334 1941,2163,2397,2643,2901,3171,3453,3747,4053,4371,4701,5043,5397,
%U A224334 5763,6141,6531,6933,7347,7773,8211,8661,9123,9597,10083,10581,11091,11613,12147
%N A224334 Number of idempotent 3 X 3 0..n matrices of rank 2.
%C A224334 Row 3 of A224333.
%H A224334 R. H. Hardin, <a href="/A224334/b224334.txt">Table of n, a(n) for n = 1..210</a>
%H A224334 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A224334 a(n) = 6*n^2 + 12*n + 3.
%F A224334 From _Colin Barker_, Feb 23 2018: (Start)
%F A224334 G.f.: 3*x*(7 - 4*x + x^2) / (1 - x)^3.
%F A224334 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A224334 (End)
%e A224334 Some solutions for n=3:
%e A224334 ..1..2..0....1..0..0....1..0..0....1..0..1....1..0..2....0..0..0....0..0..0
%e A224334 ..0..0..0....1..0..2....0..1..0....0..1..3....0..1..2....3..1..0....1..1..0
%e A224334 ..0..1..1....0..0..1....0..0..0....0..0..0....0..0..0....1..0..1....2..0..1
%o A224334 (PARI) a(n) = 6*n^2 + 12*n + 3 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A224334 (PARI) Vec(3*x*(7 - 4*x + x^2) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, Feb 23 2018
%Y A224334 Cf. A224333.
%K A224334 nonn,easy
%O A224334 1,1
%A A224334 _R. H. Hardin_, formula via _M. F. Hasler_ _William J. Keith_ and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013