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

1, 1, 1, 2, 4, 2, 4, 12, 12, 4, 8, 39, 67, 39, 8, 16, 131, 386, 386, 131, 16, 32, 444, 2333, 4191, 2333, 444, 32, 64, 1516, 14438, 47974, 47974, 14438, 1516, 64, 128, 5195, 90729, 572023, 1086791, 572023, 90729, 5195, 128, 256, 17847, 576616, 6996566, 25619209

Offset

1,4

Comments

Table starts

...1.....1........2...........4.............8..............16..............32

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

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

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

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

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

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

..64..5195...576616....86779948...15142087661...2755743447572.510116487796210

.128.17847..3692697..1085281623..372666202588.133330360329762

.256.61424.23768052.13635536887.9201018090832

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

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

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

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

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

Example

Some solutions for n=4 k=4
..0..0..0..1....0..1..0..2....0..1..1..0....0..1..2..2....0..1..0..1
..0..0..0..0....2..0..2..0....1..1..1..2....1..0..2..2....2..0..1..0
..0..2..1..0....1..2..1..1....1..1..1..1....0..2..1..0....1..2..0..2
..0..0..0..0....2..0..1..1....0..1..1..1....2..1..2..1....2..1..2..1

Crossrefs

Column 1 is A000079(n-2)

Sequence in context: A241108 A151706 A055372 * A198285 A136620 A139548

Adjacent sequences: A241075 A241076 A241077 * A241079 A241080 A241081

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 15 2014

Status

approved