A280961 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 9, 4, 11, 42, 42, 11, 30, 205, 241, 205, 30, 82, 997, 1554, 1554, 997, 82, 224, 4850, 9899, 14106, 9899, 4850, 224, 612, 23593, 63085, 126267, 126267, 63085, 23593, 612, 1672, 114769, 402077, 1121528, 1599234, 1121528, 402077, 114769, 1672, 4568

Offset

1,2

Comments

Table starts

....1.......2.........4.........11...........30............82...........224

....2.......9........42........205..........997..........4850.........23593

....4......42.......241.......1554.........9899.........63085........402077

...11.....205......1554......14106.......126267.......1121528.......9986376

...30.....997......9899.....126267......1599234......20029500.....251270618

...82....4850.....63085....1121528.....20029500.....346289502....6052621154

..224...23593....402077....9986376....251270618....6052621154..148137367471

..612..114769...2562733...88940022...3152475854..105777297118.3624578433814

.1672..558298..16334111..791997382..39530438497.1846875100200

.4568.2715861.104108376.7052519878.495721552160

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) +2*a(n-2) for n>4

k=2: a(n) = 4*a(n-1) +4*a(n-2) +a(n-3) for n>4

k=3: [order 12] for n>16

k=4: [order 54] for n>57

Example

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

Crossrefs

Column 1 is A021006(n-3).

Sequence in context: A264128 A176159 A280859 * A280362 A241130 A019822

Adjacent sequences: A280958 A280959 A280960 * A280962 A280963 A280964

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 11 2017

Status

approved