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A222381 Sum of neighbor maps: number of n X 2 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 2 array.

%I A222381 #9 Mar 15 2018 06:46:16
%S A222381 2,16,64,232,1024,4096,16224,65536,262144,1047680,4194304,16777216,
%T A222381 67104256,268435456,1073741824,4294944768,17179869184,68719476736,
%U A222381 274877800448,1099511627776,4398046511104,17592185552896,70368744177664
%N A222381 Sum of neighbor maps: number of n X 2 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 2 array.
%C A222381 Column 2 of A222386.
%H A222381 R. H. Hardin, <a href="/A222381/b222381.txt">Table of n, a(n) for n = 1..210</a>
%F A222381 Empirical: a(n) = 4*a(n-1) + 8*a(n-3) - 32*a(n-4) - 16*a(n-6) + 64*a(n-7).
%F A222381 Empirical g.f.: 2*x*(1 + 4*x - 20*x^3 + 16*x^4 + 32*x^6) / ((1 - 4*x)*(1 - 4*x^3)^2). - _Colin Barker_, Mar 15 2018
%e A222381 Some solutions for n=3:
%e A222381 ..1..0....1..1....1..0....0..1....0..1....0..0....0..0....0..1....1..0....0..1
%e A222381 ..0..0....0..0....1..1....0..1....0..1....0..1....0..0....1..0....0..0....0..0
%e A222381 ..1..0....1..1....1..1....1..1....1..0....1..0....0..1....0..0....0..1....0..1
%Y A222381 Cf. A222386.
%K A222381 nonn
%O A222381 1,1
%A A222381 _R. H. Hardin_, Feb 18 2013