A280362 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 9, 4, 11, 50, 50, 11, 30, 285, 571, 285, 30, 82, 1617, 6727, 6727, 1617, 82, 224, 9188, 78800, 164326, 78800, 9188, 224, 612, 52193, 924579, 3992071, 3992071, 924579, 52193, 612, 1672, 296511, 10844773, 97147710, 201054068, 97147710

Offset: 1

Author

R. H. Hardin, Jan 01 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

....2.......9..........50............285.............1617..............9188

....4......50.........571...........6727............78800............924579

...11.....285........6727.........164326..........3992071..........97147710

...30....1617.......78800........3992071........201054068.......10144351660

...82....9188......924579.......97147710......10144351660.....1061399606602

..224...52193....10844773.....2363431872.....511688896140...111020011111453

..612..296511...127214104....57503068637...25812250379197.11613529410292966

.1672.1684466..1492251709..1399048151083.1302084964081326

.4568.9569425.17504551617.34038954765446

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..97

Crossrefs

Column 1 is A021006(n-3).

Column 2 is A231413(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5

k=3: [order 12]

k=4: [order 44]