A188097 - OEIS

%I #11 Feb 07 2018 14:35:11

%S 65536,708,1417,3594,8274,13814,17850,20888,24117,26596,29585,35384,

%T 46623,63199,84577,111803,147698,191409,242911,306060,389117,496566,

%U 633184,808675,1039969,1339366,1719434,2201524,2822474,3618976,4632767

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

%C Column 1 of A188105.

%H R. H. Hardin, <a href="/A188097/b188097.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1)-a(n-2)+a(n-4)-2*a(n-5)+a(n-6)+a(n-8)-a(n-9) for n>15.

%F Empirical g.f.: x*(65536 - 130364*x + 65537*x^2 + 1468*x^3 - 63033*x^4 + 131224*x^5 - 67041*x^6 - 2466*x^7 - 67848*x^8 + 63218*x^9 + 1305*x^10 + 1631*x^11 + 569*x^12 + 547*x^13 + 256*x^14) / ((1 - x)*(1 - x - x^4 + x^5 - x^8)). - _Colin Barker_, Feb 07 2018

%e Some solutions for 5 X 4:

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 20 2011