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Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or vertically.
2

%I #9 Mar 19 2018 09:30:46

%S 4,16,64,240,988,3964,15844,63808,256096,1029152,4133548,16607836,

%T 66714260,268019952,1076703872,4325480208,17376731196,69807805884,

%U 280439281284,1126611556192,4525945532832,18182121542848,73043190744972

%N Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or vertically.

%C Column 1 of A232431.

%H R. H. Hardin, <a href="/A232425/b232425.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 10*a(n-2) + 11*a(n-3) - a(n-4) - 28*a(n-5) - 32*a(n-6).

%F Empirical g.f.: 4*x*(1 + 3*x + 2*x^2 - 7*x^3 - 16*x^4) / (1 - x - 10*x^2 - 11*x^3 + x^4 + 28*x^5 + 32*x^6). - _Colin Barker_, Mar 19 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

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

%Y Cf. A232431.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2013