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A197199 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,1,3,2,0 for x=0,1,2,3,4.

%I A197199 #7 Jun 02 2025 04:46:18
%S A197199 1,2,2,3,5,3,4,9,9,4,6,20,25,20,6,9,41,75,75,41,9,13,85,213,314,213,
%T A197199 85,13,19,178,621,1283,1283,621,178,19,28,369,1801,5311,7363,5311,
%U A197199 1801,369,28,41,769,5219,21803,42664,42664,21803,5219,769,41,60,1600,15133,89640
%N A197199 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,1,3,2,0 for x=0,1,2,3,4.
%C A197199 Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 2's, every 4 is next to 4 0's
%C A197199 Table starts
%C A197199 ..1....2.....3.......4........6..........9..........13............19
%C A197199 ..2....5.....9......20.......41.........85.........178...........369
%C A197199 ..3....9....25......75......213........621........1801..........5219
%C A197199 ..4...20....75.....314.....1283.......5311.......21803.........89640
%C A197199 ..6...41...213....1283.....7363......42664......247053.......1431868
%C A197199 ..9...85...621....5311....42664.....350711.....2873141......23497244
%C A197199 .13..178..1801...21803...247053....2873141....33176391.....383262156
%C A197199 .19..369..5219...89640..1431868...23497244...383262156....6258308430
%C A197199 .28..769.15133..369032..8291425..192348965..4432780869..102222467201
%C A197199 .41.1600.43867.1517961.48020216.1574634137.51234398070.1669087121069
%H A197199 R. H. Hardin, <a href="/A197199/b197199.txt">Table of n, a(n) for n = 1..220</a>
%e A197199 Some solutions for n=6 k=4
%e A197199 ..0..1..1..0....1..1..0..1....0..0..0..0....0..1..0..0....1..0..0..1
%e A197199 ..1..0..0..1....0..0..0..1....0..1..1..0....0..1..0..0....1..0..0..1
%e A197199 ..1..0..0..1....0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0
%e A197199 ..0..0..0..0....1..0..0..0....1..0..0..1....1..1..0..0....1..1..0..0
%e A197199 ..0..0..0..0....1..0..0..0....0..1..0..1....0..0..0..1....0..0..0..0
%e A197199 ..0..0..0..0....0..0..1..1....0..1..0..0....0..0..0..1....0..0..1..1
%Y A197199 Column 1 is A000930(n+1)
%Y A197199 Column 2 is A105309(n+1)
%Y A197199 Column 3 is A196431
%Y A197199 Column 4 is A196432
%K A197199 nonn,tabl
%O A197199 1,2
%A A197199 _R. H. Hardin_ Oct 11 2011