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A196945 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,0,2,3 for x=0,1,2,3,4.

%I A196945 #7 Jun 02 2025 04:38:05
%S A196945 4,38,210,1416,9199,60206,393585,2575161,16853437,110272832,721534069,
%T A196945 4721192123,30892105126,202135973690,1322631911588,8654346869839,
%U A196945 56627813612708,370531619063820,2424491930970999,15864128119739556
%N A196945 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,0,2,3 for x=0,1,2,3,4.
%C A196945 Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 3's
%C A196945 Column 3 of A196950
%H A196945 R. H. Hardin, <a href="/A196945/b196945.txt">Table of n, a(n) for n = 1..200</a>
%F A196945 Empirical: a(n) = 2*a(n-1) +17*a(n-2) +54*a(n-3) +140*a(n-4) +336*a(n-5) +294*a(n-6) -1373*a(n-7) -2487*a(n-8) -2527*a(n-9) -8223*a(n-10) -17899*a(n-11) -17316*a(n-12) -5640*a(n-13) -11863*a(n-14) -31770*a(n-15) -22665*a(n-16) +9130*a(n-17) +27976*a(n-18) +12809*a(n-19) +7193*a(n-20) +3395*a(n-21) +7688*a(n-22) -2355*a(n-23) +476*a(n-24) -420*a(n-25) +47*a(n-26) -115*a(n-27) +30*a(n-28) -5*a(n-29) for n>31
%e A196945 Some solutions for n=4
%e A196945 ..1..2..0....0..2..0....0..1..0....0..2..0....0..0..2....1..1..0....0..1..1
%e A196945 ..1..0..2....0..2..0....0..1..0....0..1..0....1..1..0....0..0..2....0..0..0
%e A196945 ..0..1..1....2..1..1....0..0..1....2..1..0....0..2..0....0..1..1....1..1..2
%e A196945 ..0..0..0....0..0..0....0..2..1....0..2..0....0..2..0....2..0..0....0..2..0
%K A196945 nonn
%O A196945 1,1
%A A196945 _R. H. Hardin_ Oct 08 2011