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A241078 T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order 6

%I

%S 1,1,1,2,4,2,4,12,12,4,8,39,67,39,8,16,131,386,386,131,16,32,444,2333,

%T 4191,2333,444,32,64,1516,14438,47974,47974,14438,1516,64,128,5195,

%U 90729,572023,1086791,572023,90729,5195,128,256,17847,576616,6996566,25619209

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order

%C Table starts

%C ...1.....1........2...........4.............8..............16..............32

%C ...1.....4.......12..........39...........131.............444............1516

%C ...2....12.......67.........386..........2333...........14438...........90729

%C ...4....39......386........4191.........47974..........572023.........6996566

%C ...8...131.....2333.......47974.......1086791........25619209.......619056332

%C ..16...444....14438......572023......25619209......1198954342.....57218949061

%C ..32..1516....90729.....6996566.....619056332.....57218949061...5383469756516

%C ..64..5195...576616....86779948...15142087661...2755743447572.510116487796210

%C .128.17847..3692697..1085281623..372666202588.133330360329762

%C .256.61424.23768052.13635536887.9201018090832

%H R. H. Hardin, <a href="/A241078/b241078.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) for n>2

%F k=2: a(n) = 6*a(n-1) -8*a(n-2) -4*a(n-3) +a(n-4) +14*a(n-5) -8*a(n-6) for n>7

%F k=3: [order 20] for n>21

%F k=4: [order 96] for n>97

%e Some solutions for n=4 k=4

%e ..0..0..0..1....0..1..0..2....0..1..1..0....0..1..2..2....0..1..0..1

%e ..0..0..0..0....2..0..2..0....1..1..1..2....1..0..2..2....2..0..1..0

%e ..0..2..1..0....1..2..1..1....1..1..1..1....0..2..1..0....1..2..0..2

%e ..0..0..0..0....2..0..1..1....0..1..1..1....2..1..2..1....2..1..2..1

%Y Column 1 is A000079(n-2)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Apr 15 2014

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Last modified August 10 09:58 EDT 2022. Contains 356039 sequences. (Running on oeis4.)