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A208639 Number of 4 X n 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 A208639 #9 Jul 05 2018 09:12:40
%S A208639 8,34,95,225,494,1042,2149,4375,8840,17784,35687,71509,143170,286510,
%T A208639 573209,1146627,2293484,4587220,9174715,18349729,36699782,73399914,
%U A208639 146800205,293600815,587202064,1174404592,2348809679,4697619885
%N A208639 Number of 4 X n 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 A208639 Row 4 of A208637.
%H A208639 R. H. Hardin, <a href="/A208639/b208639.txt">Table of n, a(n) for n = 1..210</a>
%F A208639 Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>5.
%F A208639 Conjectures from _Colin Barker_, Jul 05 2018: (Start)
%F A208639 G.f.: x*(8 - 6*x - 3*x^2 + 2*x^4) / ((1 - x)^3*(1 - 2*x)).
%F A208639 a(n) = (-42 + 35*2^n - 13*n - n^2) / 2 for n>1.
%F A208639 (End)
%e A208639 Some solutions for n=4:
%e A208639 ..0..1..0..1....0..1..0..1....0..0..0..1....0..1..1..1....0..0..1..0
%e A208639 ..1..0..1..0....0..1..0..0....1..1..0..0....1..0..0..0....1..0..1..1
%e A208639 ..0..1..0..1....0..1..1..1....0..1..1..1....0..1..1..1....0..1..0..1
%e A208639 ..0..1..0..1....1..0..0..1....0..0..0..0....1..0..0..0....0..1..0..0
%Y A208639 Cf. A208637.
%K A208639 nonn
%O A208639 1,1
%A A208639 _R. H. Hardin_, Feb 29 2012