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A224525 Number of idempotent 3 X 3 0..n matrices of rank 1.

%I A224525 #20 Dec 15 2019 21:56:57
%S A224525 27,69,123,195,273,375,477,603,735,885,1035,1221,1395,1593,1803,2031,
%T A224525 2253,2511,2757,3039,3321,3615,3909,4251,4575,4917,5271,5649,6015,
%U A224525 6429,6819,7245,7671,8109,8559,9051,9513,9999,10497,11031,11541,12099,12633
%N A224525 Number of idempotent 3 X 3 0..n matrices of rank 1.
%C A224525 Row 3 of A224524.
%H A224525 Robert Israel, <a href="/A224525/b224525.txt">Table of n, a(n) for n = 1..10000</a> (first 80 terms from R. H. Hardin)
%F A224525 a(n) = 6*n^2 + 18*n + 3 + 6 * A002541(n). - _Robert Israel_, Dec 15 2019
%e A224525 Some solutions for n=3:
%e A224525   0 1 0   1 3 2   0 1 0   1 3 1   0 0 0   0 0 0   1 0 0
%e A224525   0 1 0   0 0 0   0 1 0   0 0 0   0 1 2   3 0 3   1 0 0
%e A224525   0 3 0   0 0 0   0 2 0   0 0 0   0 0 0   1 0 1   2 0 0
%p A224525 f:= k -> 6*k^2 + 18*k + 3 + 6 * add(floor(k/m),m=2..k):
%p A224525 map(f, [$1..50]); # _Robert Israel_, Dec 15 2019
%Y A224525 Cf. A002541, A224524.
%K A224525 nonn
%O A224525 1,1
%A A224525 _R. H. Hardin_, Apr 09 2013