A186460 - OEIS

%I #9 Apr 18 2018 06:26:02

%S 245,292,590,945,1681,2377,4121,5633,8893,11977,19037,27133,43249,

%T 63485,98801,146333,225061,336241,513933,771609,1174525,1768605,

%U 2685617,4051469,6143169,9277789,14055269,21241521,32162333,48626537,73602781

%N Number of (n+1) X 8 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 7 of A186462.

%H R. H. Hardin, <a href="/A186460/b186460.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>13.

%F Empirical g.f.: x*(245 - 198*x + 6*x^2 + 255*x^3 - 115*x^4 - 144*x^5 + 369*x^6 - 547*x^7 - 36*x^8 - 640*x^9 + 484*x^10 - 300*x^11 + 784*x^12) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 3 X 8:

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

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

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

%Y Cf. A186462.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011