A280859 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 9, 4, 11, 29, 29, 11, 30, 110, 46, 110, 30, 82, 442, 96, 96, 442, 82, 224, 1708, 256, 124, 256, 1708, 224, 612, 6596, 678, 216, 216, 678, 6596, 612, 1672, 25624, 1698, 462, 282, 462, 1698, 25624, 1672, 4568, 99432, 4358, 1005, 491, 491, 1005, 4358

Offset

1,2

Comments

Table starts

....1......2.....4...11...30...82..224...612..1672...4568...12480...34096

....2......9....29..110..442.1708.6596.25624.99432.385584.1495696.5802080

....4.....29....46...96..256..678.1698..4358.11218..28650...73354..188066

...11....110....96..124..216..462.1005..2010..3907...7756...15749...31804

...30....442...256..216..282..491..968..1857..3220...5281....8574...14339

...82...1708...678..462..491..712.1202..2268..4220...7108...11240...17330

..224...6596..1698.1005..968.1202.1738..2877..5244...9569...15872...24653

..612..25624..4358.2010.1857.2268.2877..4124..6722..12044...21713...35572

.1672..99432.11218.3907.3220.4220.5244..6722..9562..15351...27000...48087

.4568.385584.28650.7756.5281.7108.9569.12044.15351..21752...34547...59836

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

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) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5

k=3: a(n) = 2*a(n-1) +4*a(n-3) -a(n-4) +2*a(n-6) -2*a(n-7) for n>9

k=4: [order 12] for n>16

k=5: [order 12] for n>18

k=6: [order 16] for n>22

k=7: [order 23] for n>29

Example

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

Crossrefs

Column 1 is A021006(n-3).

Sequence in context: A165251 A264128 A176159 * A280961 A280362 A241130

Adjacent sequences: A280856 A280857 A280858 * A280860 A280861 A280862

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 09 2017

Status

approved