A274803 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

1, 1, 1, 2, 3, 2, 4, 8, 8, 4, 8, 22, 30, 22, 8, 16, 60, 112, 112, 60, 16, 32, 164, 420, 596, 420, 164, 32, 64, 448, 1572, 3104, 3104, 1572, 448, 64, 128, 1224, 5888, 16328, 22988, 16328, 5888, 1224, 128, 256, 3344, 22048, 85504, 169328, 169328, 85504, 22048, 3344

Offset

1,4

Comments

Table starts

...1....1......2........4.........8..........16...........32.............64

...1....3......8.......22........60.........164..........448...........1224

...2....8.....30......112.......420........1572.........5888..........22048

...4...22....112......596......3104.......16328........85504.........448656

...8...60....420.....3104.....22988......169328......1252608........9243332

..16..164...1572....16328....169328.....1774372.....18476064......193292660

..32..448...5888....85504...1252608....18476064....273764292.....4044928780

..64.1224..22048...448656...9243332...193292660...4044928780....85071335388

.128.3344..82568..2352080..68301192..2016460140..59936952948..1784175028356

.256.9136.309200.12335680.504334580.21072173792.886462457880.37524080122192

Links

R. H. Hardin, Table of n, a(n) for n = 1..449

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 2*a(n-1) +15*a(n-2) +11*a(n-3) -2*a(n-4) -2*a(n-5)

k=5: a(n) = 2*a(n-1) +35*a(n-2) +42*a(n-3) -41*a(n-4) -60*a(n-5) -23*a(n-6) -2*a(n-7)

k=6: [order 14] for n>15

k=7: [order 25] for n>26

Example

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

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A028859(n-1).

Sequence in context: A105070 A154578 A059576 * A274749 A247936 A231150

Adjacent sequences: A274800 A274801 A274802 * A274804 A274805 A274806

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 07 2016

Status

approved