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A207302 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207302 #10 Jun 21 2018 14:29:53
%S A207302 13,169,665,1759,3773,7093,12169,19515,29709,43393,61273,84119,112765,
%T A207302 148109,191113,242803,304269,376665,461209,559183,671933,800869,
%U A207302 947465,1113259,1299853,1508913,1742169,2001415,2288509,2605373,2953993,3336419
%N A207302 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207302 Column 5 of A207305.
%H A207302 R. H. Hardin, <a href="/A207302/b207302.txt">Table of n, a(n) for n = 1..210</a>
%F A207302 Empirical: a(n) = (8/3)*n^4 + (49/3)*n^3 + (16/3)*n^2 - (43/3)*n + 3.
%F A207302 Conjectures from _Colin Barker_, Jun 21 2018: (Start)
%F A207302 G.f.: x*(13 + 104*x - 50*x^2 - 6*x^3 + 3*x^4) / (1 - x)^5.
%F A207302 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A207302 (End)
%e A207302 Some solutions for n=4:
%e A207302 ..1..1..1..1..0....1..0..0..1..1....1..1..0..0..1....1..0..0..1..0
%e A207302 ..0..1..0..0..1....0..1..0..0..1....0..1..0..0..1....0..0..1..0..0
%e A207302 ..0..1..0..0..1....0..1..0..0..1....0..1..0..0..1....1..0..0..1..0
%e A207302 ..0..1..0..0..1....0..1..0..0..1....0..1..0..0..1....1..0..0..1..0
%Y A207302 Cf. A207305.
%K A207302 nonn
%O A207302 1,1
%A A207302 _R. H. Hardin_, Feb 16 2012