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Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
1

%I #8 Jan 14 2019 09:01:28

%S 24,174,1086,6300,34890,187224,982086,5063964,25764066,129678528,

%T 646978302,3204131172,15769455258,77195600520,376136512950,

%U 1825265294892,8825528262738,42536536932432,204425809550958,979908028544244

%N Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

%H R. H. Hardin, <a href="/A268623/b268623.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).

%F Empirical g.f.: 6*x*(4 - 11*x + 7*x^2 + x^3) / (1 - 5*x + 2*x^2)^2. - _Colin Barker_, Jan 14 2019

%e Some solutions for n=6:

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

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

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

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

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

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

%Y Column 3 of A268628.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 09 2016