A275090 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

1, 2, 2, 3, 14, 5, 6, 36, 81, 14, 12, 96, 192, 486, 41, 24, 288, 508, 1024, 2916, 122, 48, 864, 1680, 3088, 5440, 17496, 365, 96, 2592, 5304, 12816, 18440, 29120, 104976, 1094, 192, 7776, 17184, 53132, 87924, 111900, 155904, 629856, 3281, 384, 23328, 54484

Offset: 1

Author

R. H. Hardin, Jul 16 2016

Keywords

• nonn
• tabl

Comments

Table starts

....1........2........3.........6.........12..........24............48

....2.......14.......36........96........288.........864..........2592

....5.......81......192.......508.......1680........5304.........17184

...14......486.....1024......3088......12816.......53132........232156

...41.....2916.....5440.....18440......87924......510680.......2934756

..122....17496....29120....111900.....647648.....5038428......38872396

..365...104976...155904....675600....4706400....48675088.....512150588

.1094...629856...834176...4094240...34281472...477786368....6767371752

.3281..3779136..4463424..24794560..248629316..4669603380...89090043684

.9842.22674816.23883904.150165020.1807849760.45596095332.1174911360788

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..336

Crossrefs

Column 1 is A007051(n-1).

Row 1 is A003945(n-2).

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>10

k=4: [order 14] for n>15

k=5: [order 27] for n>28

k=6: [order 64] for n>66

Empirical for row n:

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

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

n=3: [order 36] for n>38

n=4: [order 84] for n>88