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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.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 11 2017
STATUS
approved