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Number of 2 X n 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
1

%I #7 Feb 08 2019 12:32:07

%S 0,3,19,136,935,6381,43478,296105,2016307,13729364,93484479,636542307,

%T 4334257038,29512224731,200950553535,1368284654492,9316734157423,

%U 63438214373401,431954692843542,2941205998493005,20026852048660187

%N Number of 2 X n 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%H R. H. Hardin, <a href="/A278189/b278189.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 16*a(n-2) + 9*a(n-3) - 12*a(n-4) + 5*a(n-5) + 7*a(n-6) - 4*a(n-7).

%F Empirical g.f.: x^2*(3 - 2*x)*(1 - x + x^2)^2 / (1 - 9*x + 16*x^2 - 9*x^3 + 12*x^4 - 5*x^5 - 7*x^6 + 4*x^7). - _Colin Barker_, Feb 08 2019

%e Some solutions for n=4:

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

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

%Y Row 2 of A278188.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 14 2016