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A197403 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

%I A197403 #9 Mar 01 2018 14:31:28
%S A197403 3,9,20,71,227,664,2107,6675,20696,65029,205057,643930,2026105,
%T A197403 6384135,20104382,63329883,199576691,628932096,1982100085,6247388117,
%U A197403 19691746204,62069757373,195654894641,616749232724,1944155102539,6128552692107
%N A197403 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.
%C A197403 Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.
%C A197403 Column 2 of A197409.
%H A197403 R. H. Hardin, <a href="/A197403/b197403.txt">Table of n, a(n) for n = 1..200</a>
%F A197403 Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 7*a(n-3) - 10*a(n-4) - 39*a(n-5) - 30*a(n-6) - 12*a(n-7) + 5*a(n-8) + 2*a(n-9).
%F A197403 Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 9*x^3 - 3*x^4 + 8*x^5 + 2*x^6) / (1 - 2*x - 4*x^2 - 7*x^3 + 10*x^4 + 39*x^5 + 30*x^6 + 12*x^7 - 5*x^8 - 2*x^9). - _Colin Barker_, Mar 01 2018
%e A197403 Some solutions for n=4:
%e A197403 ..1..0....1..0....1..0....0..1....1..0....0..0....0..1....0..1....1..0....1..0
%e A197403 ..3..1....3..1....1..0....1..2....2..0....1..1....1..1....0..1....2..0....1..2
%e A197403 ..1..1....1..2....2..1....1..0....1..0....2..1....1..0....2..1....1..1....0..1
%e A197403 ..0..0....0..0....0..1....1..0....2..1....0..0....1..0....1..0....0..1....0..1
%Y A197403 Cf. A197409.
%K A197403 nonn
%O A197403 1,1
%A A197403 _R. H. Hardin_, Oct 14 2011