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%I #9 Oct 16 2018 05:42:15
%S 204,2504,30536,371976,4530424,55175944,671983416,8184025736,
%T 99672501944,1213902270984,14784004509496,180053035925896,
%U 2192849421966264,26706512126351624,325256163423006776,3961265003235768456
%N Number of (n+1) X (1+1) 0..3 arrays with each 2 X 2 subblock having the number of clockwise edge increases less than or equal to the number of counterclockwise edge increases.
%H R. H. Hardin, <a href="/A234789/b234789.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 15*a(n-1) - 36*a(n-2) + 20*a(n-3).
%F Conjectures from _Colin Barker_, Oct 16 2018: (Start)
%F G.f.: 4*x*(51 - 139*x + 80*x^2) / ((1 - 2*x)*(1 - 13*x + 10*x^2)).
%F a(n) = (1/129)*2^(-1-n)*(-129*2^(1+2*n) + (2193-191*sqrt(129))*(13-sqrt(129))^n + (13+sqrt(129))^n*(2193+191*sqrt(129))).
%F (End)
%e Some solutions for n=3:
%e ..2..3....1..2....2..0....2..3....1..0....1..0....2..1....0..1....3..2....1..0
%e ..2..3....0..1....2..0....3..1....3..2....3..2....0..2....0..1....2..0....2..0
%e ..2..2....2..0....3..2....3..1....0..0....2..0....2..1....0..1....2..3....3..0
%e ..0..0....1..3....2..0....0..0....1..1....2..3....2..0....2..3....3..3....1..3
%Y Column 1 of A234796.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2013
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