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%I #10 Sep 04 2018 12:21:23
%S 5737,4129,4868,5371,5727,7090,9090,11457,14037,17836,23484,31351,
%T 41643,55578,74998,102125,139377,190396,260660,357879,492171,677302,
%U 932510,1284753,1771097,2442380,3368672,4647011,6411491,8847050,12208690
%N Number of (n+3) X 9 0..2 matrices with each 4 X 4 subblock idempotent.
%H R. H. Hardin, <a href="/A224726/b224726.txt">Table of n, a(n) for n = 1..122</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 2*a(n-4) - 5*a(n-5) + 4*a(n-6) - a(n-7) - a(n-8) + 2*a(n-9) - a(n-10) for n>12.
%F Empirical g.f.: x*(5737 - 13082*x + 9692*x^2 - 2583*x^3 - 11385*x^4 + 21581*x^5 - 12409*x^6 + 2549*x^7 + 5641*x^8 - 8500*x^9 + 2710*x^10 + 37*x^11) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 - x - x^4)). - _Colin Barker_, Sep 04 2018
%e Some solutions for n=2:
%e ..1..0..0..0..1..0..0..0..2....1..0..0..0..0..0..0..0..0
%e ..1..0..0..0..1..0..0..0..0....1..0..0..0..0..0..0..0..0
%e ..0..0..0..0..1..0..0..0..0....0..0..0..0..0..0..0..0..0
%e ..1..0..0..0..1..0..0..0..1....1..0..0..0..0..0..0..0..0
%e ..2..0..0..0..1..0..0..0..1....2..0..0..0..0..0..0..0..1
%Y Column 6 of A224728.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 16 2013
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