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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
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 21:51 EDT 2022. Contains 354830 sequences. (Running on oeis4.)