A186561 - OEIS

%I #12 Apr 19 2018 03:28:04

%S 721,173,401,1411,2617,3379,4033,4795,6361,10443,17153,26995,43177,

%T 66139,98497,151699,231881,350539,543249,835843,1270105,1958875,

%U 3007777,4577331,7041321,10810763,16490033,25335715,38890105,59403259,91177217

%N Number of (n+2) X 4 0..2 arrays with every 3 X 3 subblock commuting with each horizontal and vertical neighbor 3 X 3 subblock.

%C Column 2 of A186568.

%H R. H. Hardin, <a href="/A186561/b186561.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 2*a(n-7) for n>10.

%F Empirical g.f.: x*(721 - 1269*x + 776*x^2 - 660*x^3 + 2734*x^4 - 1996*x^5 - 3114*x^6 + 812*x^7 + 1236*x^8 + 712*x^9) / ((1 - x)*(1 - x - 2*x^3 + 2*x^4 - 2*x^6)). - _Colin Barker_, Apr 18 2018

%e Some solutions for 6 X 4:

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

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

%e   0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0     0 0 0 0

%e   0 0 0 0     0 0 0 0     2 0 0 0     0 0 0 0     0 0 0 0

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

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

%Y Cf. A186568.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 23 2011