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

Author

R. H. Hardin, Jul 26 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A003945(n-2).

Row 1 is A007051(n-1).

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