A186583 - OEIS

%I #8 Apr 18 2018 14:31:50

%S 38608,1991,5879,39757,115699,149305,156259,160945,165739,171145,

%T 185131,230017,470139,778697,1118323,1529121,2339979,3298521,4347171,

%U 5627937,8189067,11662681,15995763,21614673,31416027,44959433,62319075,84811905

%N Number of (n+3) X 6 0..2 arrays with every 4 X 4 subblock commuting with each horizontal and vertical neighbor 4 X 4 subblock.

%C Column 3 of A186589.

%H R. H. Hardin, <a href="/A186583/b186583.txt">Table of n, a(n) for n = 1..150</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>13

%F Empirical g.f.: x*(38608 - 75225*x + 40505*x^2 + 29990*x^3 - 35152*x^4 + 108114*x^5 - 107662*x^6 - 62248*x^7 - 161236*x^8 + 158518*x^9 + 54108*x^10 - 32320*x^11 + 43136*x^12) / ((1 - x)*(1 - x - 2*x^4 + 2*x^5 - 2*x^8)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 5 X 6:

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

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

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

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

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

%Y Cf. A186589.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2011