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A208634 Number of n X 5 0..1 arrays with new values 0..1 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 A208634 #9 Jul 05 2018 08:34:46
%S A208634 16,47,150,494,1652,5572,18888,64216,218704,745616,2543520,8679776,
%T A208634 29625920,101131840,345250944,1178690944,4024163584,13739075840,
%U A208634 46907582976,160151393792,546788836352,1866849412096,6373813684224
%N A208634 Number of n X 5 0..1 arrays with new values 0..1 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 A208634 Column 5 of A208637.
%H A208634 R. H. Hardin, <a href="/A208634/b208634.txt">Table of n, a(n) for n = 1..210</a>
%F A208634 Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + 4*a(n-3).
%F A208634 Conjectures from _Colin Barker_, Jul 05 2018: (Start)
%F A208634 G.f.: x*(16 - 49*x + 28*x^2) / ((1 - 2*x)*(1 - 4*x + 2*x^2)).
%F A208634 a(n) = (3*2^(1+n) + (11-2*sqrt(2))*(2-sqrt(2))^n + (2+sqrt(2))^n*(11+2*sqrt(2))) / 4.
%F A208634 (End)
%e A208634 Some solutions for n=4:
%e A208634 ..0..0..1..1..0....0..1..1..0..0....0..1..0..0..1....0..1..1..0..0
%e A208634 ..1..0..0..1..1....0..0..1..1..0....1..0..1..0..0....1..0..1..1..1
%e A208634 ..1..1..0..0..0....1..0..0..1..1....1..0..1..1..1....0..1..0..0..1
%e A208634 ..0..1..1..1..0....0..1..0..0..0....1..0..0..0..1....1..0..1..0..1
%Y A208634 Cf. A208637.
%K A208634 nonn
%O A208634 1,1
%A A208634 _R. H. Hardin_, Feb 29 2012