A275401 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

1, 2, 2, 5, 9, 3, 14, 54, 16, 6, 41, 324, 84, 31, 12, 122, 1944, 444, 178, 63, 24, 365, 11664, 2344, 1011, 394, 129, 48, 1094, 69984, 12376, 5758, 2404, 1017, 260, 96, 3281, 419904, 65344, 32771, 14884, 8122, 2645, 534, 192, 9842, 2519424, 345008, 186538, 91849

Offset

1,2

Comments

Table starts

...1....2.....5......14.......41.......122.........365.........1094

...2....9....54.....324.....1944.....11664.......69984.......419904

...3...16....84.....444.....2344.....12376.......65344.......345008

...6...31...178....1011.....5758.....32771......186538......1061795

..12...63...394....2404....14884.....91849......566331......3495079

..24..129..1017....8122....65045....518049.....4142271.....33102260

..48..260..2645...27373...283169...2940064....30551417....317215507

..96..534..6980...94065..1266905..17159883...232200615...3146508594

.192.1083.18464..323306..5656712.100110527..1766745035..31272546310

.384.2210.48959.1109170.25396322.587134035.13518543301.312946900074

Links

R. H. Hardin, Table of n, a(n) for n = 1..243

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) for n>3

k=2: [order 9] for n>10

k=3: [order 24] for n>28

k=4: [order 65] for n>69

Empirical for row n:

n=1: a(n) = 4*a(n-1) -3*a(n-2)

n=2: a(n) = 6*a(n-1) for n>2

n=3: a(n) = 4*a(n-1) +6*a(n-2) +4*a(n-3)

n=4: a(n) = 3*a(n-1) +11*a(n-2) +25*a(n-3) +2*a(n-4) -24*a(n-5) for n>6

n=5: [order 9] for n>10

n=6: [order 16] for n>17

n=7: [order 21] for n>22

Example

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

Crossrefs

Column 1 is A003945(n-2).

Row 1 is A007051(n-1).

Sequence in context: A040009 A227527 A275504 * A011273 A274068 A274065

Adjacent sequences: A275398 A275399 A275400 * A275402 A275403 A275404

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 26 2016

Status

approved