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

Author

R. H. Hardin, Jul 07 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-2).

Column 2 is A028859(n-1).

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