A186455 - OEIS

%I #9 Apr 17 2018 14:13:39

%S 21,30,51,88,128,197,292,457,688,1058,1589,2424,3651,5552,8376,12709,

%T 19192,29085,43952,66562,100629,152332,230359,348632,527296,797909,

%U 1206940,1826193,2762528,4179698,6322981,9566352,14472171,21895248

%N Number of (n+1) X 3 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 2 of A186462.

%H R. H. Hardin, <a href="/A186455/b186455.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.

%F Empirical g.f.: x*(21 - 12*x - 9*x^2 + 28*x^3 - 30*x^4 + 4*x^5 + 2*x^6 + 4*x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 17 2018

%e Some solutions for 5 X 3:

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

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

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

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

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

%Y Cf. A186462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011