A186457 - OEIS

%I #8 Apr 17 2018 14:10:02

%S 61,88,162,309,449,673,945,1493,2201,3473,5177,7993,11949,18289,27473,

%T 41857,63041,95765,144473,219105,330905,501353,757677,1147281,1734561,

%U 2625569,3970577,6008917,9088537,13752497,20802745,31475673,47614509

%N Number of (n+1) X 5 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 4 of A186462.

%H R. H. Hardin, <a href="/A186457/b186457.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>10.

%F Empirical g.f.: x*(61 - 34*x - 14*x^2 + 107*x^3 - 115*x^4 - 16*x^5 - 19*x^6 + 45*x^7 - 28*x^8 + 64*x^9) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 17 2018

%e Some solutions for 3 X 5:

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

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

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

%Y Cf. A186462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011