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%I #10 Feb 17 2018 10:26:42
%S 189,300,398,573,793,1126,1608,2343,3471,5236,8022,12457,19553,30950,
%T 49300,78895,126679,203888,328702,530537,856989,1385070,2239388,
%U 3621563,5857823,9476016,15330218,24802353,40128421,64926346,105050052,169971387
%N Number of (n+1) X 7 0..2 matrices with each 2 X 2 subblock idempotent.
%C Column 6 of A224676.
%H R. H. Hardin, <a href="/A224674/b224674.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n > 6.
%F Empirical g.f.: x*(189 - 456*x + 143*x^2 + 292*x^3 - 187*x^4 + 10*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Feb 17 2018
%e Some solutions for n=3:
%e 1 0 1 0 1 0 2 1 1 1 1 1 1 2 0 0 0 0 1 0 0
%e 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1
%e 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1
%e 0 0 1 0 1 0 1 2 1 1 1 1 1 1 0 0 0 0 1 0 1
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2013
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