A238923 - OEIS

%I #8 Oct 24 2018 14:26:36

%S 12,36,144,540,2052,7776,29484,111780,423792,1606716,6091524,23094720,

%T 87558732,331960356,1258557264,4771552860,18090330372,68585649696,

%U 260027940204,985840769700,3737606129712,14170340698236,53723840483844

%N Number of (n+1) X (1+1) 0..3 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.

%H R. H. Hardin, <a href="/A238923/b238923.txt">Table of n, a(n) for n = 1..210</a>

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

%F Conjectures from _Colin Barker_, Oct 24 2018: (Start)

%F G.f.: 12*x / (1 - 3*x - 3*x^2).

%F a(n) = (-4)*(sqrt(3/7)*(((3-sqrt(21))/2)^n - ((3+sqrt(21))/2)^n)).

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A238929.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 07 2014