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A208402 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

%I A208402 #9 Jul 02 2018 10:16:09
%S A208402 2,15,187,2795,43947,700075,11188907,178973355,2863377067,45813246635,
%T A208402 733008800427,11728128223915,187650001250987,3002399818689195,
%U A208402 48038396293720747,768614337478306475,12297829386768001707
%N A208402 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
%C A208402 Column 2 of A208408.
%H A208402 R. H. Hardin, <a href="/A208402/b208402.txt">Table of n, a(n) for n = 1..210</a>
%F A208402 Empirical: a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
%F A208402 Conjectures from _Colin Barker_, Jul 02 2018: (Start)
%F A208402 G.f.: x*(2 - 27*x + 40*x^2) / ((1 - x)*(1 - 4*x)*(1 - 16*x)).
%F A208402 a(n) = (8 + 3*2^(1+2*n) + 16^n) / 24.
%F A208402 (End)
%e A208402 Some solutions for n=4:
%e A208402 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0
%e A208402 ..0..0....0..1....1..0....0..0....0..0....0..1....0..1....0..0....1..1....1..0
%e A208402 ..1..1....0..0....0..2....0..1....1..2....1..0....0..0....1..0....0..0....2..0
%e A208402 ..2..0....1..0....2..0....1..0....3..2....1..1....0..2....2..2....0..1....1..2
%Y A208402 Cf. A208408.
%K A208402 nonn
%O A208402 1,1
%A A208402 _R. H. Hardin_, Feb 26 2012