A190026 - OEIS

%I #8 May 03 2018 07:02:18

%S 112,45,79,155,235,295,355,423,531,740,1037,1434,1992,2706,3628,4920,

%T 6665,9015,12293,16738,22710,30902,42006,56987,77466,105302,142987,

%U 194362,264198,358864,487699,662831,900478,1223669,1662993,2259498

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

%C Column 2 of A190033.

%H R. H. Hardin, <a href="/A190026/b190026.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5) +a(n-6) -a(n-7) for n>10.

%F Empirical g.f.: x*(112 - 179*x + 101*x^2 - 70*x^3 + 183*x^4 - 121*x^5 - 154*x^6 + 71*x^7 + 26*x^8 + 25*x^9) / ((1 - x)*(1 - x - x^3 + x^4 - x^6)). - _Colin Barker_, May 03 2018

%e Some solutions for 6 X 4:

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

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

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

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

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

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

%Y Cf. A190033.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011