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Number of black-square subarrays of (n+2) X (3+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
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%I #7 Sep 23 2018 09:07:20

%S 8,16,102,232,1682,3768,27106,60824,437930,982552,7073698,15870936,

%T 114260634,256361112,1845635570,4140964568,29812290666,66888415128,

%U 481553712898,1080439106264,7778468998714,17452180031640,125644509294994

%N Number of black-square subarrays of (n+2) X (3+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

%H R. H. Hardin, <a href="/A230930/b230930.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-2) + 3*a(n-4) - 10*a(n-6) + 24*a(n-8) - 16*a(n-10).

%F Empirical g.f.: 2*x*(4 + 8*x - 13*x^2 - 12*x^3 + 13*x^4 + 4*x^5 - 16*x^6 + 8*x^8) / (1 - 16*x^2 - 3*x^4 + 10*x^6 - 24*x^8 + 16*x^10). - _Colin Barker_, Sep 23 2018

%e Some solutions for n=4:

%e ..x..0..x..0..x....x..0..x..0..x....x..0..x..0..x....x..0..x..0..x

%e ..1..x..1..x..3....3..x..1..x..3....1..x..3..x..1....1..x..1..x..3

%e ..x..2..x..0..x....x..0..x..2..x....x..2..x..2..x....x..2..x..0..x

%e ..3..x..1..x..3....3..x..1..x..3....0..x..0..x..1....1..x..3..x..1

%e ..x..0..x..2..x....x..2..x..0..x....x..1..x..3..x....x..0..x..2..x

%e ..3..x..3..x..1....1..x..1..x..3....0..x..2..x..2....3..x..1..x..1

%Y Column 3 of A230935.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 01 2013