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%I #8 Sep 01 2018 12:36:30
%S 628,630,782,906,1202,1609,2091,2817,3895,5397,7564,10745,15361,22074,
%T 31895,46256,67251,97985,142995,208912,305472,446948,654244,958000,
%U 1403129,2055448,3011414,4412397,6465584,9474619,13884516,20347476
%N Number of (n+2) X 7 0..2 matrices with each 3 X 3 subblock idempotent.
%C Column 5 of A224606.
%H R. H. Hardin, <a href="/A224603/b224603.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*(628 - 1882*x + 2030*x^2 - 1582*x^3 + 1632*x^4 - 1037*x^5 + 203*x^6 + 5*x^7) / ((1 - x)^3*(1 - x - x^3)). - _Colin Barker_, Sep 01 2018
%e Some solutions for n=3:
%e ..1..1..1..0..0..0..0....1..0..0..0..0..0..0....0..1..0..0..0..0..0
%e ..0..0..0..0..0..0..0....1..0..0..0..0..0..0....0..1..0..0..0..0..1
%e ..0..0..0..0..0..0..0....1..0..0..0..0..0..0....0..1..0..0..0..0..1
%e ..0..0..0..0..0..0..1....2..0..0..0..0..0..0....0..1..0..0..0..0..1
%e ..0..0..0..0..0..0..1....0..0..0..0..1..1..1....0..2..0..0..0..0..1
%Y Cf. A224606.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 11 2013