%I #8 Jun 29 2018 08:05:00

%S 14,768,43344,2445264,137947632,7782199824,439026252912,

%T 24767296501776,1397226183866736,78823339024454928,

%U 4446752320207192176,250859789016717819408,14152043831975777230704,798375640062491402594064

%N Number of n X 4 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

%C Column 4 of A208258.

%H R. H. Hardin, <a href="/A208254/b208254.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 61*a(n-1) - 266*a(n-2) + 416*a(n-3) - 256*a(n-4) for n>5.

%F Empirical g.f.: 2*x*(7 - 43*x + 110*x^2 - 128*x^3 + 64*x^4) / (1 - 61*x + 266*x^2 - 416*x^3 + 256*x^4). - _Colin Barker_, Jun 29 2018

%e Some solutions for n=4

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

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

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

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

%Y Cf. A208258.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 24 2012