A186582 - OEIS

%I #8 Apr 18 2018 14:34:09

%S 8824,827,1991,12263,42313,79015,98893,104983,108805,112735,118765,

%T 143799,230021,395695,605325,865143,1254981,1811583,2468157,3275175,

%U 4514677,6419055,8942637,12286743,17275493,24707199,34690461,47928807

%N Number of (n+3) X 5 0..2 arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

%C Column 2 of A186589.

%H R. H. Hardin, <a href="/A186582/b186582.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-4) - 4*a(n-5) + 2*a(n-6) + 2*a(n-8) - 2*a(n-9) for n>14.

%F Empirical g.f.: x*(8824 - 16821*x + 9161*x^2 + 9108*x^3 + 2130*x^4 + 40294*x^5 - 35146*x^6 - 32004*x^7 - 59472*x^8 + 2798*x^9 + 33420*x^10 + 26036*x^11 + 5624*x^12 + 5832*x^13) / ((1 - x)*(1 - x - 2*x^4 + 2*x^5 - 2*x^8)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 7 X 5:

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

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

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

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

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

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

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

%Y Cf. A186589.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2011