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A220172 Sum of neighbor maps: number of n X 1 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 n X 1 array.

%I A220172 #10 Feb 18 2018 08:46:54
%S A220172 2,2,8,16,24,64,128,232,512,1024,1984,4096,8192,16224,32768,65536,
%T A220172 130688,262144,524288,1047680,2097152,4194304,8386560,16777216,
%U A220172 33554432,67104256,134217728,268435456,536860672,1073741824,2147483648,4294944768
%N A220172 Sum of neighbor maps: number of n X 1 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, vertical and antidiagonal neighbors in a random 0..2 n X 1 array.
%C A220172 Column 1 of A220177.
%H A220172 R. H. Hardin, <a href="/A220172/b220172.txt">Table of n, a(n) for n = 1..210</a>
%F A220172 Empirical: a(n) = 2*a(n-1) +4*a(n-3) -8*a(n-4) -4*a(n-6) +8*a(n-7).
%F A220172 Empirical g.f.: 2*(1 - x + 2*x^2 - 4*x^3 + 4*x^6) / ((1 - 2*x)*(1 - 2*x^3)^2). - _Colin Barker_, Feb 18 2018
%e A220172 All solutions for n=3:
%e A220172 ..1....0....1....1....0....0....0....1
%e A220172 ..1....1....0....1....0....0....1....0
%e A220172 ..0....0....1....1....0....1....1....0
%K A220172 nonn
%O A220172 1,1
%A A220172 _R. H. Hardin_, Dec 06 2012