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%I #11 Nov 05 2018 06:33:59
%S 71,197,545,1501,4145,11441,31577,87161,240581,664051,1832917,5059221,
%T 13964475,38544783,106391413,293661867,810566283,2237327253,
%U 6175476757,17045567707,47049222251,129865390965,358454804639,989407924729
%N Number of length n+3 0..2 arrays with some pair in every consecutive four terms totalling exactly 2.
%H R. H. Hardin, <a href="/A245945/b245945.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) + a(n-8) + a(n-9).
%F Empirical g.f.: x*(71 + 55*x + 9*x^2 - 54*x^3 - 73*x^4 - 57*x^5 - 15*x^6 + 36*x^7 + 27*x^8) / ((1 - x)*(1 - x - 3*x^2 - 4*x^3 - 3*x^4 - x^5 + x^6 + 2*x^7 + x^8)). - _Colin Barker_, Nov 05 2018
%e Some solutions for n=8:
%e ..0....1....1....1....2....1....0....0....1....1....2....1....0....0....1....2
%e ..1....1....2....1....0....2....2....1....0....2....0....0....0....1....1....0
%e ..2....2....0....2....1....0....2....0....2....2....0....1....2....1....0....0
%e ..0....1....0....0....1....1....0....2....0....1....2....2....0....0....1....1
%e ..1....2....1....1....1....0....2....1....0....0....2....1....1....2....1....2
%e ..0....1....1....0....1....1....2....0....1....1....0....0....0....2....1....1
%e ..2....2....1....2....2....1....1....0....1....2....2....1....1....1....2....0
%e ..2....0....1....2....1....0....0....1....0....2....0....0....2....0....1....2
%e ..0....1....0....0....2....0....1....1....0....0....2....2....0....2....2....0
%e ..0....1....1....1....0....2....1....2....2....2....2....1....2....0....1....0
%e ..2....2....1....1....0....2....2....1....2....1....1....0....0....0....2....2
%Y Column 2 of A245950.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 08 2014
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