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A196680 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

%I A196680 #7 Jun 02 2025 04:30:10
%S A196680 4,20,58,292,1235,5186,22461,96256,413032,1780597,7673860,33017186,
%T A196680 142219489,612618957,2638803566,11367909928,48973948677,210982341958,
%U A196680 908945163931,3915948771137,16870934284560,72684969189462
%N A196680 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.
%C A196680 Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 3's
%C A196680 Column 3 of A196685
%H A196680 R. H. Hardin, <a href="/A196680/b196680.txt">Table of n, a(n) for n = 1..200</a>
%F A196680 Empirical: a(n) = 4*a(n-1) +4*a(n-2) -6*a(n-3) +10*a(n-4) -60*a(n-5) -160*a(n-6) -634*a(n-7) -1583*a(n-8) +297*a(n-9) +2182*a(n-10) +9602*a(n-11) +42284*a(n-12) +39581*a(n-13) +18230*a(n-14) +15645*a(n-15) -60179*a(n-16) -28875*a(n-17) +1218*a(n-18) -23566*a(n-19) +46466*a(n-20) -35766*a(n-21) -50232*a(n-22) -41220*a(n-23) -33792*a(n-24) +26772*a(n-25) +17644*a(n-26) +18228*a(n-27) +6120*a(n-28) +4281*a(n-29) +3612*a(n-30) +772*a(n-31) -1467*a(n-32) -815*a(n-33) -304*a(n-34) -271*a(n-35) -35*a(n-36) +19*a(n-37) +3*a(n-38)
%e A196680 Some solutions for n=4
%e A196680 ..1..1..0....0..0..0....1..0..1....1..2..1....1..1..0....0..0..1....1..1..1
%e A196680 ..0..1..1....1..2..1....2..1..2....0..0..0....0..1..2....0..0..2....0..0..0
%e A196680 ..0..1..2....1..0..1....0..2..0....0..0..0....0..1..1....1..2..1....1..2..1
%e A196680 ..1..1..0....1..0..1....1..1..0....0..0..0....1..1..0....1..0..0....1..0..1
%K A196680 nonn
%O A196680 1,1
%A A196680 _R. H. Hardin_ Oct 05 2011