%I #4 Apr 19 2014 12:34:47

%S 2,59,2344,95144,3875244,157912026,6435036610,262234101215,

%T 10686305830308,435477843275035,17746165666239258,723174326871008607,

%U 29470090437788760318,1200936203282125872968,48939373545548944414862

%N Number of nX3 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order

%C Column 3 of A241328

%H R. H. Hardin, <a href="/A241324/b241324.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 45*a(n-1) -171*a(n-2) -57*a(n-3) -1321*a(n-4) +2701*a(n-5) +10837*a(n-6) +5209*a(n-7) +13262*a(n-8) -1578*a(n-9) -7272*a(n-10) -5706*a(n-11) -17487*a(n-12) -2511*a(n-13) +4779*a(n-14) -729*a(n-15)

%e Some solutions for n=4

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

%e ..0..2..3....3..0..0....0..2..0....2..0..1....3..0..1....1..2..3....2..1..1

%e ..3..2..3....1..0..0....1..3..0....0..1..0....0..2..3....1..2..0....2..3..0

%e ..2..1..3....1..2..3....0..1..0....3..0..2....0..2..3....0..3..0....3..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 19 2014