A186467 - OEIS

%I #8 Apr 18 2018 10:28:04

%S 367,562,1203,3186,4875,9834,14883,31866,51057,105398,174289,347428,

%T 588058,1145866,1976438,3787644,6625638,12540516,22170114,41575892,

%U 74087098,137980420,247343794,458282956,825184634,1523024532,2751516210

%N Number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

%C Column 4 of A186472.

%H R. H. Hardin, <a href="/A186467/b186467.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>13.

%F Empirical g.f.: x*(367 - 172*x - 288*x^2 + 1686*x^3 - 1920*x^4 + 196*x^5 - 604*x^6 + 1428*x^7 - 1350*x^8 + 1364*x^9 + 36*x^10 - 18*x^11 + 9*x^12) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 3 X 5:

%e ..0..0..0..1..1....1..2..0..2..0....1..2..0..0..0....2..0..0..0..0

%e ..0..0..0..0..1....2..0..2..0..2....2..0..2..0..0....0..2..0..0..0

%e ..2..0..0..0..0....0..2..0..2..1....0..2..0..2..0....0..0..2..0..0

%Y Cf. A186472.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2011