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A222382 Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

%I A222382 #8 Aug 16 2018 08:58:20
%S A222382 8,48,512,3968,32768,261376,2097152,16773120,134217728,1073721344,
%T A222382 8589934592,68719378432,549755813888,4398046052352,35184372088832,
%U A222382 281474974613504,2251799813685248,18014398500044800,144115188075855872
%N A222382 Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.
%C A222382 Column 3 of A222386.
%H A222382 R. H. Hardin, <a href="/A222382/b222382.txt">Table of n, a(n) for n = 1..210</a>
%F A222382 Empirical: a(n) = 8*a(n-1) + 8*a(n-2) - 64*a(n-3) - 16*a(n-4) + 128*a(n-5).
%F A222382 Empirical g.f.: 8*x*(1 - 2*x + 8*x^2 + 16*x^4) / ((1 - 2*x)^2*(1 + 2*x)^2*(1 - 8*x)). - _Colin Barker_, Aug 16 2018
%e A222382 Some solutions for n=3:
%e A222382 ..1..1..1....1..1..1....0..1..0....1..1..1....0..0..1....0..1..1....0..1..1
%e A222382 ..1..1..1....1..1..0....0..1..0....1..0..0....0..1..0....1..0..0....1..0..0
%e A222382 ..1..1..0....0..1..1....1..0..0....0..1..1....1..1..1....1..0..1....1..0..0
%Y A222382 Cf. A222386.
%K A222382 nonn
%O A222382 1,1
%A A222382 _R. H. Hardin_, Feb 18 2013