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A209095 Number of n X 3 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 or right-upward antidiagonal neighbors.

%I A209095 #9 Jul 08 2018 10:48:22
%S A209095 5,76,1326,23248,407832,7154944,125526240,2202232576,38635976064,
%T A209095 677829707776,11891846929920,208630607073280,3660216151873536,
%U A209095 64214845877125120,1126585496573239296,19764820171301257216
%N A209095 Number of n X 3 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 or right-upward antidiagonal neighbors.
%C A209095 Column 3 of A209100.
%H A209095 R. H. Hardin, <a href="/A209095/b209095.txt">Table of n, a(n) for n = 1..210</a>
%F A209095 Empirical: a(n) = 20*a(n-1) - 44*a(n-2) + 16*a(n-3) for n>4.
%F A209095 Conjectures from _Colin Barker_, Jul 08 2018: (Start)
%F A209095 G.f.: x*(5 - 4*x)*(1 - 4*x + 2*x^2) / ((1 - 2*x)*(1 - 18*x + 8*x^2)).
%F A209095 a(n) = 2^(n-3) + ((9-sqrt(73))^n*(-25+sqrt(73)) + (9+sqrt(73))^n*(25+sqrt(73))) / (16*sqrt(73)) for n>1.
%F A209095 (End)
%e A209095 Some solutions for n=4:
%e A209095 ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..1..2
%e A209095 ..1..2..1....1..1..1....1..1..2....2..0..0....1..1..2....1..0..2....1..2..1
%e A209095 ..1..0..1....2..0..0....2..0..0....2..1..0....0..0..0....1..1..2....0..2..1
%e A209095 ..2..1..2....1..2..2....1..1..1....2..2..2....1..2..0....0..0..1....1..2..2
%Y A209095 Cf. A209100.
%K A209095 nonn
%O A209095 1,1
%A A209095 _R. H. Hardin_, Mar 05 2012