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Half the number of n X 3 binary arrays with no element equal to a strict majority of its king-move neighbors.
1

%I #9 Mar 28 2018 07:21:39

%S 1,5,11,29,89,245,669,1891,5297,14753,41267,115455,322661,902047,

%T 2522301,7051895,19715891,55124449,154123101,430912643,1204794989,

%U 3368504981,9418046333,26332052309,73622187095,205841375745,575515014243

%N Half the number of n X 3 binary arrays with no element equal to a strict majority of its king-move neighbors.

%C Column 3 of A183386.

%H R. H. Hardin, <a href="/A183382/b183382.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 6*a(n-3) - 13*a(n-4) + 3*a(n-5) - 2*a(n-6) + 6*a(n-7) + 4*a(n-8) + 5*a(n-9) - 4*a(n-10) - 2*a(n-11).

%F Empirical g.f.: x*(1 + 2*x - 2*x^2)*(1 - x - x^2 - x^3 - x^5 + 3*x^6 + x^7 + x^8) / (1 - 4*x + 4*x^2 - 6*x^3 + 13*x^4 - 3*x^5 + 2*x^6 - 6*x^7 - 4*x^8 - 5*x^9 + 4*x^10 + 2*x^11). - _Colin Barker_, Mar 28 2018

%e Some solutions for 5 X 3:

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

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

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

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

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

%Y Cf. A183386.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 04 2011