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Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
1

%I #8 Jan 18 2019 09:57:53

%S 0,24,48,216,672,2208,6912,21408,65280,196992,589056,1748352,5156352,

%T 15124992,44156928,128383488,371908608,1073879040,3091820544,

%U 8878479360,25435250688,72710922240,207448571904,590798364672,1679765078016

%N Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%H R. H. Hardin, <a href="/A269036/b269036.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4).

%F Empirical g.f.: 24*x^2*(1 - x)^2 / (1 - 2*x - 2*x^2)^2. - _Colin Barker_, Jan 18 2019

%e Some solutions for n=4:

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

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

%Y Row 2 of A269035.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 18 2016