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A196295 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

%I A196295 #7 Jun 02 2025 04:20:19
%S A196295 4,20,58,290,1201,4988,21344,90150,381754,1621695,6890299,29235310,
%T A196295 124148208,527208582,2238746157,9507860508,40379986769,171493157818,
%U A196295 728338492990,3093321027043,13137679999737,55797480705949
%N A196295 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.
%C A196295 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 4's, every 4 is next to 4 2's
%C A196295 Column 3 of A196300
%H A196295 R. H. Hardin, <a href="/A196295/b196295.txt">Table of n, a(n) for n = 1..200</a>
%F A196295 Empirical: a(n) = 4*a(n-1) +3*a(n-2) -2*a(n-3) -3*a(n-4) -28*a(n-5) -108*a(n-6) -553*a(n-7) -1487*a(n-8) -406*a(n-9) +1679*a(n-10) +7367*a(n-11) +29776*a(n-12) +40461*a(n-13) +40921*a(n-14) +25939*a(n-15) +4942*a(n-16) -5887*a(n-17) -21877*a(n-18) -27360*a(n-19) -19016*a(n-20) +284*a(n-21) +3863*a(n-22) -2168*a(n-23) -3302*a(n-24) +3474*a(n-25) +1158*a(n-26) -171*a(n-27) -1312*a(n-28) +650*a(n-29) -96*a(n-30) +70*a(n-31) -18*a(n-32)
%e A196295 Some solutions for n=4
%e A196295 ..0..2..1....0..1..1....1..1..0....0..0..1....0..0..1....0..0..0....0..1..1
%e A196295 ..2..1..0....1..1..0....0..2..1....0..0..2....2..1..2....2..1..1....1..2..0
%e A196295 ..1..1..1....2..1..1....0..2..1....0..2..1....1..1..2....1..1..1....1..0..0
%e A196295 ..0..0..1....0..0..1....1..1..0....1..1..0....0..0..1....0..0..0....2..1..1
%K A196295 nonn
%O A196295 1,1
%A A196295 _R. H. Hardin_ Sep 30 2011