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%I #9 Mar 17 2018 07:10:09
%S 0,2,2,10,22,70,186,538,1494,4230,11866,33434,94006,264582,744314,
%T 2094362,5892502,16579462,46647706,131248794,369281782,1039014534,
%U 2923376826,8225233690,23142568790,65114084998,183205408986,515467935386
%N Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
%C Column 2 of A230899.
%H R. H. Hardin, <a href="/A230893/b230893.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3).
%F Empirical g.f.: 2*x^2*(1 - x) / (1 - 2*x - 3*x^2 + 2*x^3). - _Colin Barker_, Mar 17 2018
%e All solutions for n=4:
%e ..0..1....0..1....0..3....0..3....0..1....0..3....0..1....0..3....0..3....0..1
%e ..3..2....3..2....1..2....1..2....3..2....1..2....3..2....1..2....1..2....3..2
%e ..0..3....2..3....2..1....2..3....1..0....3..0....2..1....0..3....0..1....0..1
%e ..1..2....1..0....3..0....1..0....2..3....2..1....3..0....1..2....3..2....3..2
%Y Cf. A230899.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 31 2013