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%I #7 Oct 06 2015 22:02:46
%S 1,2,29,388,4170,41423,388998,3528126,31206553,270945278,2318825000,
%T 19619049541,164448364546,1367755750914,11301610770163,92861669073522,
%U 759320826126174,6182626278886591,50153160109476104,405492870969390486
%N 1/12 the number of (n+1) X 3 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 2 of A183729.
%H R. H. Hardin, <a href="/A183722/b183722.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=14*a(n-1)-36*a(n-2)-115*a(n-3)+125*a(n-4)+164*a(n-5)-155*a(n-6)-29*a(n-7)+34*a(n-8)+a(n-9)-2*a(n-10).
%e Some solutions with the first block increasing clockwise for 5 X 3:
%e ..2..4..3....4..0..3....1..4..2....1..2..1....1..2..1....1..3..2....3..5..4
%e ..1..0..1....2..1..2....0..5..0....0..5..0....0..3..0....5..4..5....2..1..2
%e ..2..5..2....3..0..3....1..4..1....1..4..1....5..4..5....0..3..0....3..0..3
%e ..3..4..3....4..5..4....2..3..2....2..3..2....0..2..0....1..2..1....4..5..4
%e ..1..5..1....1..0..2....0..4..0....5..4..1....5..3..4....4..3..5....2..1..2
%e ...
%e ...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...
%e ...L..R.......L..R.......L..R.......L..R.......R..L.......L..R.......L..R...
%e ...L..R.......L..R.......L..R.......L..R.......L..R.......L..R.......L..R...
%e ...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 06 2011
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