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

Author

R. H. Hardin, Jan 09 2017

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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) -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