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%I #12 Sep 27 2018 04:58:37
%S 1,5,15,46,156,507,1637,5338,17401,56648,184384,600287,1954546,
%T 6363740,20718710,67455328,219621081,715042212,2328028685,7579574414,
%U 24677521267,80344901649,261586345777,851670870944,2772863697333,9027869180467
%N Number of n X 3 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,3,2,1,2 for x=0,1,2,3,4.
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 2's.
%C Column 3 of A197242.
%H R. H. Hardin, <a href="/A197237/b197237.txt">Table of n, a(n) for n = 1..200</a>
%H Robert Israel, <a href="/A197237/a197237.pdf">Maple-assisted proof of empirical formula</a>
%F Empirical: a(n) = 2*a(n-1) + 8*a(n-3) + 11*a(n-4) + 17*a(n-5) + 11*a(n-6) + 5*a(n-7) - 6*a(n-8) - 16*a(n-9) - 15*a(n-10) - 3*a(n-11) + a(n-13).
%F Empirical formula verified (see link). - _Robert Israel_, Sep 26 2018
%e Some solutions for n=4:
%e 1 3 1 0 0 0 2 2 2 0 0 1 0 0 0 0 0 0 1 3 1
%e 0 1 0 0 1 0 2 0 2 1 1 3 1 3 1 0 1 0 0 1 0
%e 0 1 0 1 3 1 2 0 2 3 1 1 0 1 0 0 3 1 0 2 2
%e 1 3 1 0 0 0 2 2 2 1 0 0 0 0 0 0 1 0 0 2 2
%p f:= gfun:-rectoproc({a(n) = 2*a(n-1) +8*a(n-3) +11*a(n-4) +17*a(n-5) +11*a(n-6) +5*a(n-7) -6*a(n-8) -16*a(n-9) -15*a(n-10) -3*a(n-11) +a(n-13), seq(a(i)=[1, 5, 15, 46, 156, 507, 1637, 5338, 17401, 56648, 184384, 600287, 1954546][i],i=1..13)}, a(n), remember):
%p map(f, [$1..30]); # _Robert Israel_, Sep 26 2018
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 12 2011
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