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%I #7 Oct 06 2015 22:03:13
%S 12,29,124,1790,30939,525895,8439116,130610844,1967828529,29070445544,
%T 422988995515,6081228134954,86580348551185,1222760452357981,
%U 17151917685428842,239202719875959959,3319294757106439138
%N 1/12 the number of (n+1) X 4 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 3 of A183729.
%H R. H. Hardin, <a href="/A183723/b183723.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=22*a(n-1)-8*a(n-2)-2038*a(n-3)+4849*a(n-4)+60267*a(n-5)-204061*a(n-6)-712337*a(n-7)+3325947*a(n-8)+3154325*a(n-9)-27076488*a(n-10)+4020761*a(n-11)+122413547*a(n-12)-93348742*a(n-13)-325835425*a(n-14)+402806197*a(n-15)+514609889*a(n-16)-925150963*a(n-17)-439511369*a(n-18)+1310144478*a(n-19)+86470889*a(n-20)-1199641648*a(n-21)+219926386*a(n-22)+717789749*a(n-23)-257447414*a(n-24)-276848427*a(n-25)+139910715*a(n-26)+66195171*a(n-27)-44059046*a(n-28)-8998172*a(n-29)+8348721*a(n-30)+522019*a(n-31)-936761*a(n-32)+15437*a(n-33)+58686*a(n-34)-3505*a(n-35)-1816*a(n-36)+147*a(n-37)+21*a(n-38)-2*a(n-39).
%e Some solutions with the first block increasing clockwise for 3 X 4:
%e ..4..5..4..3....1..2..1..0....3..5..4..3....4..5..0..5....0..1..0..5
%e ..1..0..1..2....0..3..4..5....1..0..1..2....3..2..1..2....3..2..3..4
%e ..4..5..4..3....1..2..1..0....3..5..4..3....4..5..0..4....4..1..0..5
%e ...
%e ...R..L..L.......R..L..L.......R..L..L.......R..R..L.......R..L..L...
%e ...L..R..R.......L..R..R.......L..R..R.......L..L..R.......L..R..R...
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2011
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