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A220932 Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

%I A220932 #9 Mar 13 2018 16:33:46
%S A220932 2,16,92,556,3332,19996,119972,719836,4319012,25914076,155484452,
%T A220932 932906716,5597440292,33584641756,201507850532,1209047103196,
%U A220932 7254282619172,43525695715036,261154174290212,1566925045741276
%N A220932 Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.
%C A220932 Column 3 of A220935.
%H A220932 R. H. Hardin, <a href="/A220932/b220932.txt">Table of n, a(n) for n = 1..210</a>
%F A220932 Empirical: a(n) = 5*a(n-1) + 6*a(n-2).
%F A220932 Conjectures from _Colin Barker_, Mar 13 2018: (Start)
%F A220932 G.f.: 2*x*(1 + 3*x) / ((1 + x)*(1 - 6*x)).
%F A220932 a(n) = (2^n*3^(n+1) + 4) / 7 for n even.
%F A220932 a(n) = (2^n*3^(n+1) - 4) / 7 for n odd
%F A220932 (End)
%e A220932 Some solutions for n=3:
%e A220932 ..0..1..0....0..1..1....0..1..0....0..0..0....0..0..0....0..1..0....0..0..0
%e A220932 ..0..0..1....1..0..1....0..1..0....1..0..1....0..0..1....0..0..0....0..1..0
%e A220932 ..1..1..0....1..0..0....0..1..0....1..0..0....0..1..0....1..1..0....1..0..0
%Y A220932 Cf. A220935.
%K A220932 nonn
%O A220932 1,1
%A A220932 _R. H. Hardin_, Dec 25 2012