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A198180 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.

%I A198180 #7 Jun 02 2025 05:23:52
%S A198180 1,3,9,25,77,148,395,866,2346,5663,14065,34309,84252,208413,513352,
%T A198180 1266410,3117377,7679699,18927327,46639092,114949605,283220762,
%U A198180 697929906,1719783577,4237987789,10443340285,25734497336,63415169957,156267786924
%N A198180 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4.
%C A198180 Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's
%C A198180 Column 3 of A198185
%H A198180 R. H. Hardin, <a href="/A198180/b198180.txt">Table of n, a(n) for n = 1..200</a>
%F A198180 Empirical: a(n) = a(n-1) +3*a(n-2) -a(n-3) +3*a(n-4) +14*a(n-5) -a(n-6) -13*a(n-7) -17*a(n-8) -43*a(n-9) -73*a(n-10) -111*a(n-11) -70*a(n-12) -49*a(n-13) +87*a(n-14) +274*a(n-15) +424*a(n-16) +337*a(n-17) +389*a(n-18) +202*a(n-19) +184*a(n-20) -420*a(n-21) -643*a(n-22) -580*a(n-23) -287*a(n-24) -116*a(n-25) -426*a(n-26) -5*a(n-27) +80*a(n-28) +414*a(n-29) +294*a(n-30) +24*a(n-31) -12*a(n-32) -72*a(n-33) -30*a(n-34) +4*a(n-36) +4*a(n-37)
%e A198180 Some solutions for n=4
%e A198180 ..1..2..1....2..1..0....2..1..0....0..1..2....0..3..0....1..2..1....2..1..0
%e A198180 ..0..3..0....1..0..1....1..1..2....2..1..1....3..0..3....1..2..1....1..0..3
%e A198180 ..3..0..1....1..2..2....0..1..1....1..1..0....0..3..0....1..2..1....0..3..0
%e A198180 ..0..1..2....0..1..1....1..2..0....0..2..1....1..2..1....1..2..1....1..2..1
%K A198180 nonn
%O A198180 1,2
%A A198180 _R. H. Hardin_ Oct 21 2011