%I #5 Mar 31 2012 12:36:25

%S 5,17,50,335,866,2942,13277,56237,228881,862148,3323631,13251496,

%T 53662892,215087507,848846709,3350015319,13308176712,53085757815,

%U 211514954392,840367835992,3336205123509,13258112907409,52741016443951

%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,4,1,3 for x=0,1,2,3,4

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

%C Column 4 of A196314

%H R. H. Hardin, <a href="/A196310/b196310.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) -4*a(n-2) -2*a(n-3) +29*a(n-4) +44*a(n-5) -365*a(n-6) -563*a(n-7) -486*a(n-8) +18*a(n-9) +424*a(n-10) -8576*a(n-11) +29598*a(n-12) +95820*a(n-13) +200698*a(n-14) +364105*a(n-15) +598354*a(n-16) -292736*a(n-17) -2334999*a(n-18) -6081591*a(n-19) -14964178*a(n-20) -11648855*a(n-21) -17466704*a(n-22) -25028551*a(n-23) +14094341*a(n-24) +14352761*a(n-25) +579801*a(n-26) -1186235*a(n-27) -1593062*a(n-28) -225384*a(n-29) +3130755*a(n-30) +1386124*a(n-31) -405424*a(n-32) -609745*a(n-33) -394802*a(n-34) +8031*a(n-35) +36199*a(n-36) +2246*a(n-37) +2252*a(n-38) +720*a(n-39)

%e Some solutions for n=5

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

%e ..0..1..1..1....0..1..1..0....1..3..1..1....0..1..1..1....0..3..1..0

%e ..0..1..1..0....0..3..1..0....0..1..1..0....0..1..3..0....1..1..1..1

%e ..0..1..3..0....0..1..3..1....0..1..3..0....0..1..1..0....1..0..0..1

%e ..1..3..1..0....1..1..0..1....0..1..1..0....1..3..1..0....1..0..0..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 01 2011