cp's OEIS Frontend

A208393 Number of 2 X n 0..2 arrays with new values 0..2 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 A208393 #9 Jul 02 2018 10:08:37
%S A208393 2,14,117,1017,8838,76806,667476,5800644,50410008,438083928,
%T A208393 3807131472,33085555344,287527231584,2498731184736,21715012867392,
%U A208393 188712490047552,1639989997584768,14252194920963456,123857499353216256
%N A208393 Number of 2 X n 0..2 arrays with new values 0..2 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 A208393 Row 2 of A208392.
%H A208393 R. H. Hardin, <a href="/A208393/b208393.txt">Table of n, a(n) for n = 1..210</a>
%F A208393 Empirical: a(n) = 8*a(n-1) + 6*a(n-2) for n>4.
%F A208393 Conjectures from _Colin Barker_, Jul 02 2018: (Start)
%F A208393 G.f.: x*(1 + x)*(2 - 4*x - 3*x^2) / (1 - 8*x - 6*x^2).
%F A208393 a(n) = ((4-sqrt(22))^n*(-2+sqrt(22)) + (2+sqrt(22))*(4+sqrt(22))^n) / (8*sqrt(22)) for n>2.
%F A208393 (End)
%e A208393 Some solutions for n=4:
%e A208393 ..0..0..0..0....0..0..0..0....0..1..1..0....0..0..1..2....0..0..0..0
%e A208393 ..1..2..2..2....0..1..0..2....1..2..1..2....0..2..2..0....0..1..1..2
%Y A208393 Cf. A208392.
%K A208393 nonn
%O A208393 1,1
%A A208393 _R. H. Hardin_, Feb 25 2012