A275266 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,-1) and new values introduced in order 0..2.

1, 2, 2, 5, 9, 5, 14, 54, 24, 14, 41, 324, 128, 64, 41, 122, 1944, 688, 396, 172, 122, 365, 11664, 3728, 2564, 1440, 476, 365, 1094, 69984, 20224, 17036, 13156, 5676, 1320, 1094, 3281, 419904, 109760, 114184, 126420, 73012, 22844, 3672, 3281, 9842

Offset

1,2

Comments

Table starts

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

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

....5....24.....128......688.......3728........20224.........109760

...14....64.....396.....2564......17036.......114184.........767400

...41...172....1440....13156.....126420......1224088.......11894712

..122...476....5676....73012....1020324.....14005180......194398028

..365..1320...22844...409728....8391716....161725644.....3224773976

.1094..3672...93968..2315520...70863268...1922952988....56045462432

.3281.10220..389820.13124196..603245904..22903224024...981633748272

.9842.28472.1626348.74374784.5149743348.271600215464.17187870741644

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical for column k:

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

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

k=3: [order 14] for n>17

k=4: [order 43] for n>47

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) = 6*a(n-1) -2*a(n-2) -6*a(n-3) for n>4

n=4: a(n) = 8*a(n-1) -7*a(n-2) -9*a(n-3) -8*a(n-4) -12*a(n-5) +16*a(n-6) for n>7

n=5: [order 18] for n>19

n=6: [order 24] for n>26

n=7: [order 43] for n>45

Example

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

Crossrefs

Column 1 is A007051(n-1).

Row 1 is A007051(n-1).

Sequence in context: A274068 A274065 A233073 * A223387 A278386 A262614

Adjacent sequences: A275263 A275264 A275265 * A275267 A275268 A275269

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 21 2016

Status

approved