A186459 - OEIS

%I #8 Apr 17 2018 14:26:32

%S 151,197,362,673,1061,1693,2377,3677,5073,7977,11533,18221,26957,

%T 41729,62105,95205,142645,217581,327233,497481,749885,1137821,1717565,

%U 2603089,3932825,5956277,9003685,13630333,20610673,31193705,47177837,71391309

%N Number of (n+1) X 7 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 6 of A186462.

%H R. H. Hardin, <a href="/A186459/b186459.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>12.

%F Empirical g.f.: x*(151 - 105*x - 32*x^2 + 251*x^3 - 193*x^4 + 52*x^5 - 190*x^6 + 61*x^7 - 344*x^8 + 260*x^9 - 128*x^10 + 324*x^11) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 17 2018

%e Some solutions for 3 X 7:

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

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

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

%Y Cf. A186462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011