A222382 - OEIS

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 #8 Aug 16 2018 08:58:20

%S 8,48,512,3968,32768,261376,2097152,16773120,134217728,1073721344,

%T 8589934592,68719378432,549755813888,4398046052352,35184372088832,

%U 281474974613504,2251799813685248,18014398500044800,144115188075855872

%N 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 Column 3 of A222386.

%H R. H. Hardin, <a href="/A222382/b222382.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) + 8*a(n-2) - 64*a(n-3) - 16*a(n-4) + 128*a(n-5).

%F 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 Some solutions for n=3:

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

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

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

%Y Cf. A222386.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 18 2013