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Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.
1

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

%S 0,1,6,56,324,2196,13328,83680,512752,3161248,19384848,118981520,

%T 729388016,4471790032,27407876144,167983235088,1029494729904,

%U 6309251897744,38665450224432,236955187985936,1452135101851056

%N Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.

%C Row 2 of A221400.

%H R. H. Hardin, <a href="/A221401/b221401.txt">Table of n, a(n) for n = 1..69</a>

%F Empirical: a(n) = 7*a(n-1) + 6*a(n-2) - 74*a(n-3) + 8*a(n-4) + 132*a(n-5) - 72*a(n-6) - 24*a(n-7) + 16*a(n-8).

%F Empirical g.f.: x^2*(1 - 2*x)*(1 + x + 10*x^2 - 10*x^3 + 8*x^4 - 8*x^5) / ((1 - 4*x + 2*x^2)*(1 + 2*x - 2*x^2)*(1 - 5*x - 8*x^2 + 6*x^3 + 4*x^4)). - _Colin Barker_, Aug 05 2018

%e All solutions for n=3:

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

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

%Y Cf. A221400.

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 15 2013