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%I #11 Apr 04 2018 10:48:01
%S 0,1,12,87,537,3070,16731,88331,455804,2311983,11571209,57295330,
%T 281223411,1370286715,6635743136,31964799247,153273890393,
%U 732031932806,3483896304443,16529018119643,78202676604548,369073777749215
%N 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.
%C Column 1 of A183729.
%H R. H. Hardin, <a href="/A183721/b183721.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6).
%F Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - _Colin Barker_, Apr 04 2018
%e All solutions with the first block increasing clockwise for 3 X 2:
%e ..3..4....1..2....4..5....2..3....5..0....0..1
%e ..2..5....0..3....3..0....1..4....4..1....5..2
%e ..1..0....5..4....2..1....0..5....3..2....4..3
%e ...
%e ...R.......R.......R.......R.......R.......R...
%e ...R.......R.......R.......R.......R.......R...
%Y Cf. A183729.
%K nonn
%O 1,3
%A _R. H. Hardin_, Jan 06 2011
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