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Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2.
1

%I #8 Aug 05 2018 08:21:51

%S 7,119,2008,33873,571358,9637322,162555929,2741882383,46248186229,

%T 780082534460,13157894317753,221938287447408,3743501973486176,

%U 63142809559541159,1065049364666447387,17964518161956501475

%N Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2.

%C Column 3 of A221328.

%H R. H. Hardin, <a href="/A221323/b221323.txt">Table of n, a(n) for n = 1..69</a>

%F Empirical: a(n) = 23*a(n-1) - 110*a(n-2) + 111*a(n-3) - 6*a(n-4) - 8*a(n-5).

%F Empirical g.f.: x*(1 - x)*(7 - 35*x + 6*x^2 + 8*x^3) / (1 - 23*x + 110*x^2 - 111*x^3 + 6*x^4 + 8*x^5). - _Colin Barker_, Aug 05 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A221328.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2013