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%I #7 Aug 31 2018 06:38:02
%S 50,70,113,172,263,418,669,1064,1699,2734,4409,7108,11471,18538,29973,
%T 48464,78379,126790,205121,331852,536903,868690,1405533,2274152,
%U 3679603,5953678,9633209,15586804,25219919,40806634,66026469,106833008,172859371
%N Number of (n+2) X 3 0..1 matrices with each 3 X 3 subblock idempotent.
%C Column 1 of A224559.
%H R. H. Hardin, <a href="/A224552/b224552.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) - a(n-5) + a(n-6) for n>7.
%F Empirical g.f.: x*(50 - 80*x + 53*x^2 - 57*x^3 - 4*x^4 + 39*x^5 - 7*x^6) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)). - _Colin Barker_, Aug 31 2018
%e Some solutions for n=3:
%e ..1..0..1....0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..0
%e ..0..0..0....1..1..1....0..0..0....1..0..0....0..0..1....0..0..0....0..0..0
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1....0..0..0
%e ..1..0..1....0..0..0....1..1..1....0..1..1....0..0..1....0..0..0....0..0..0
%e ..1..0..1....1..0..1....0..0..0....0..0..0....0..0..1....0..1..1....0..0..0
%Y Cf. A224559.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 10 2013