A186565 - OEIS

%I #8 Apr 18 2018 15:24:07

%S 20056,3379,5605,12895,23389,29935,36133,44887,60493,91519,137701,

%T 205879,317293,498159,754229,1158823,1794685,2717311,4159813,6426583,

%U 9779021,14980399,23102037,35240263,53961373,83056543,126889765,194291511

%N Number of (n+2) X 8 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 6 of A186568.

%H R. H. Hardin, <a href="/A186565/b186565.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>14.

%F Empirical g.f.: x*(20056 - 36733*x + 18903*x^2 - 35048*x^3 + 76670*x^4 - 41754*x^5 - 50588*x^6 + 29502*x^7 + 10296*x^8 + 1536*x^9 - 10944*x^10 - 4800*x^11 + 21632*x^13) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 4 X 8:

%e ..1..0..0..0..0..0..0..1....2..0..0..0..0..0..1..0....0..0..0..0..2..0..0..1

%e ..0..1..0..0..0..0..0..0....0..2..0..0..0..0..0..0....0..0..0..0..0..2..0..0

%e ..0..0..1..0..0..0..0..0....0..0..2..0..0..0..0..0....1..0..0..0..0..0..2..0

%e ..2..0..0..1..0..0..0..0....1..0..0..2..0..0..0..2....0..2..0..0..0..0..0..2

%Y Cf. A186568.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2011