A196316 - OEIS

%I #8 Feb 18 2018 10:02:29

%S 1,7,10,23,57,122,275,623,1394,3133,7045,15824,35557,79901,179530,

%T 403401,906439,2036744,4576523,10283359,23106492,51919817,116662775,

%U 262138870,589020695,1323517493,2973916806,6682330407,15015060135,33738533866

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 4's.

%C Column 2 of A196322.

%H R. H. Hardin, <a href="/A196316/b196316.txt">Table of n, a(n) for n = 1..200</a>

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

%F Empirical g.f.: x*(1 + 6*x + x^2 - 3*x^3) / ((1 + x + x^2)*(1 - 2*x - x^2 + x^3)). - _Colin Barker_, Feb 18 2018

%e Some solutions for n=4:

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 01 2011