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A197404 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

%I A197404 #7 Jun 02 2025 04:53:56
%S A197404 4,20,60,358,1626,7232,34717,160988,748843,3514426,16448990,76889286,
%T A197404 359867470,1684122959,7879951514,36879246800,172597946528,
%U A197404 807735845097,3780221117751,17691605965676,82797291928191,387496301051514
%N A197404 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.
%C A197404 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 1's, every 4 is next to 4 1's
%C A197404 Column 3 of A197409
%H A197404 R. H. Hardin, <a href="/A197404/b197404.txt">Table of n, a(n) for n = 1..200</a>
%F A197404 Empirical: a(n) = 4*a(n-1) +4*a(n-2) +8*a(n-3) -37*a(n-4) -13*a(n-5) -58*a(n-6) -814*a(n-7) -2710*a(n-8) -1095*a(n-9) +6385*a(n-10) +15988*a(n-11) +42018*a(n-12) +47855*a(n-13) +32250*a(n-14) -50035*a(n-15) -77306*a(n-16) -41809*a(n-17) -25413*a(n-18) -49387*a(n-19) -14658*a(n-20) +11927*a(n-21) +12328*a(n-22) +6216*a(n-23) +17403*a(n-24) +12464*a(n-25) -363*a(n-26) +6490*a(n-27) -2100*a(n-28) +61*a(n-29) -629*a(n-30) -131*a(n-31) +42*a(n-32) +a(n-33) +a(n-34)
%e A197404 Some solutions for n=4
%e A197404 ..1..0..0....1..0..0....0..0..0....1..0..0....1..0..1....1..1..0....0..0..0
%e A197404 ..2..1..1....2..0..0....0..2..1....1..1..2....1..2..1....0..1..1....1..1..1
%e A197404 ..0..2..1....1..2..1....2..1..2....0..2..1....0..0..0....0..1..2....2..1..3
%e A197404 ..0..0..0....0..0..1....1..0..0....0..0..0....1..1..1....1..2..0....0..0..1
%K A197404 nonn
%O A197404 1,1
%A A197404 _R. H. Hardin_ Oct 14 2011