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%I #8 Sep 02 2018 06:46:34
%S 1694,1221,1455,1657,2091,2656,3308,4272,5672,7588,10325,14312,20058,
%T 28377,40512,58215,84052,121832,177116,258031,376513,550059,804293,
%U 1176775,1722562,2522335,3694335,5411860,7928889,11617642,17023637
%N Number of (n+2) X 9 0..2 matrices with each 3 X 3 subblock idempotent.
%C Column 7 of A224606.
%H R. H. Hardin, <a href="/A224605/b224605.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 3*a(n-5) - a(n-6) for n>8.
%F Empirical g.f.: x*(1694 - 5555*x + 6735*x^2 - 5307*x^3 + 4864*x^4 - 3239*x^5 + 796*x^6 + 5*x^7) / ((1 - x)^3*(1 - x - x^3)). - _Colin Barker_, Sep 02 2018
%e Some solutions for n=3:
%e ..1..1..1..1..1..1..1..1..0....1..0..0..0..0..0..0..0..0
%e ..0..0..0..0..0..0..0..0..0....1..0..0..0..0..0..0..0..2
%e ..0..0..0..0..0..0..0..0..0....1..0..0..0..0..0..0..0..1
%e ..0..0..0..0..0..0..0..0..0....2..0..0..0..0..0..0..0..1
%e ..0..0..0..0..0..1..1..1..1....2..0..0..0..0..0..0..0..1
%Y Cf. A224606.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 11 2013
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