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

Author

R. H. Hardin, Jan 11 2017

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A021006(n-3).

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