A281129 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 1, 2, 1, 2, 28, 28, 2, 8, 208, 574, 208, 8, 28, 1364, 5590, 5590, 1364, 28, 94, 8354, 48828, 75668, 48828, 8354, 94, 304, 48992, 394202, 923678, 923678, 394202, 48992, 304, 960, 278966, 3042893, 10441416, 15835126, 10441416, 3042893, 278966, 960

Offset

1,5

Comments

Table starts

....0.......0..........1............2............8............28............94

....0.......2.........28..........208.........1364..........8354.........48992

....1......28........574.........5590........48828........394202.......3042893

....2.....208.......5590........75668.......923678......10441416.....112649322

....8....1364......48828.......923678.....15835126.....250872018....3803844412

...28....8354.....394202.....10441416....250872018....5550177494..117185694820

...94...48992....3042893....112649322...3803844412..117185694820.3459450309336

..304..278966...22772368...1178277478..55967077710.2402634147622

..960.1554744..166675727..12052427112.805490418258

.2976.8524848.1199580226.121217893114

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7

k=2: a(n) = 8*a(n-1) -8*a(n-2) -30*a(n-3) -24*a(n-4) -8*a(n-5) -a(n-6)

k=3: [order 23] for n>30

Example

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

Crossrefs

Column 1 is A280279.

Sequence in context: A228690 A121721 A173476 * A136156 A191657 A155796

Adjacent sequences: A281126 A281127 A281128 * A281130 A281131 A281132

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 15 2017

Status

approved