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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.
2

%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