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%I #7 Jun 19 2021 09:48:05
%S 1,1,1,1,2,1,1,5,5,1,1,8,14,8,1,1,18,44,44,18,1,1,37,149,221,149,37,1,
%T 1,73,479,1175,1175,479,73,1,1,151,1537,5982,10210,5982,1537,151,1,1,
%U 306,4971,30940,84893,84893,30940,4971,306,1,1,621,16088,160438,706153
%N 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 4,3,2,1,0 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 0's
%C Table starts
%C .1...1.....1.......1.........1...........1.............1...............1
%C .1...2.....5.......8........18..........37............73.............151
%C .1...5....14......44.......149.........479..........1537............4971
%C .1...8....44.....221......1175........5982.........30940..........160438
%C .1..18...149....1175.....10210.......84893........706153.........5894192
%C .1..37...479....5982.....84893.....1130812......15034832.......202026037
%C .1..73..1537...30940....706153....15034832.....322715244......6984694296
%C .1.151..4971..160438...5894192...202026037....6984694296....242641943340
%C .1.306.16088..828709..49247065..2712108937..150562726618...8412809597191
%C .1.621.52020.4285218.411367276.36354079627.3245505223710.291896308327024
%H R. H. Hardin, <a href="/A197217/b197217.txt">Table of n, a(n) for n = 1..180</a>
%e Some solutions for n=6 k=4
%e ..1..3..1..0....0..1..3..1....2..2..2..0....1..3..1..0....0..1..2..2
%e ..0..1..0..0....0..0..1..0....2..0..2..0....0..1..0..0....1..3..2..2
%e ..0..1..3..1....0..0..0..1....2..1..2..2....0..0..0..0....0..1..0..1
%e ..0..0..1..0....0..1..1..3....2..3..1..2....0..1..0..0....0..0..1..3
%e ..2..2..0..0....1..3..0..1....2..1..2..2....1..3..2..2....0..1..0..1
%e ..2..2..0..0....0..1..0..0....2..2..2..0....0..1..2..2....1..3..1..0
%Y C. A197211 (k=2), A197212 (k=3), A197213 (k=4),..
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Oct 11 2011
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