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A208705 Number of n X 4 0..1 arrays with new values 0..1 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 A208705 #8 Jul 06 2018 06:04:49
%S A208705 8,100,1268,16084,204020,2587924,32826932,416398420,5281871732,
%T A208705 66998738836,849856117940,10780134577876,136742325040628,
%U A208705 1734529687216660,22001916633654068,279086797488636244
%N A208705 Number of n X 4 0..1 arrays with new values 0..1 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 A208705 Column 4 of A208709.
%H A208705 R. H. Hardin, <a href="/A208705/b208705.txt">Table of n, a(n) for n = 1..210</a>
%F A208705 Empirical: a(n) = 13*a(n-1) - 4*a(n-2).
%F A208705 Conjectures from _Colin Barker_, Jul 06 2018: (Start)
%F A208705 G.f.: 4*x*(2 - x) / (1 - 13*x + 4*x^2).
%F A208705 a(n) = (2^(-1-n)*((13-3*sqrt(17))^n*(-1+sqrt(17)) + (1+sqrt(17))*(13+3*sqrt(17))^n)) / sqrt(17).
%F A208705 (End)
%e A208705 Some solutions for n=4:
%e A208705 ..0..1..1..1....0..0..0..0....0..1..0..1....0..1..1..1....0..1..1..0
%e A208705 ..0..0..1..1....0..1..1..0....0..0..1..0....1..0..0..0....0..0..1..0
%e A208705 ..1..0..0..1....1..0..1..1....0..1..1..1....0..1..1..1....0..0..1..1
%e A208705 ..0..1..1..1....1..1..0..1....1..0..1..1....1..0..0..0....1..0..0..0
%Y A208705 Cf. A208709
%K A208705 nonn
%O A208705 1,1
%A A208705 _R. H. Hardin_, Mar 01 2012