A220172 - OEIS

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 #10 Feb 18 2018 08:46:54

%S 2,2,8,16,24,64,128,232,512,1024,1984,4096,8192,16224,32768,65536,

%T 130688,262144,524288,1047680,2097152,4194304,8386560,16777216,

%U 33554432,67104256,134217728,268435456,536860672,1073741824,2147483648,4294944768

%N 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 Column 1 of A220177.

%H R. H. Hardin, <a href="/A220172/b220172.txt">Table of n, a(n) for n = 1..210</a>

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

%F 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 All solutions for n=3:

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 06 2012