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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A021006(n-3).

Column 2 is A231413(n-1).

Sequence in context: A176159 A280859 A280961 * A241130 A019822 A322765

Adjacent sequences: A280359 A280360 A280361 * A280363 A280364 A280365

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2017

Status

approved