A275142 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.

1, 1, 2, 2, 6, 5, 4, 16, 36, 14, 8, 48, 80, 216, 41, 16, 144, 224, 400, 1296, 122, 32, 432, 528, 1088, 2000, 7776, 365, 64, 1296, 1216, 2320, 5248, 10000, 46656, 1094, 128, 3888, 2816, 6464, 9744, 25344, 50000, 279936, 3281, 256, 11664, 6544, 17872, 32384, 41360

Offset: 1

Author

R. H. Hardin, Jul 17 2016

Keywords

• nonn
• tabl

Comments

Table starts

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

....2........6......16.......48......144.......432......1296.......3888

....5.......36......80......224......528......1216......2816.......6544

...14......216.....400.....1088.....2320......6464.....17872......49792

...41.....1296....2000.....5248.....9744.....32384....107472.....362176

..122.....7776...10000....25344....41360....165568....663904....2695808

..365....46656...50000...122368...175120....841536...4055152...19906560

.1094...279936..250000...590848...741904...4283968..24875600..147762240

.3281..1679616.1250000..2852864..3142672..21800000.152379136.1093999424

.9842.10077696.6250000.13774848.13312656.110943552.933805200.8109111360

Examples

			Some solutions for n=5 k=4
..0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..2..1. .0..1..2..0
..2..0..1..0. .0..2..1..2. .2..0..1..2. .2..0..2..0. .0..1..2..0
..2..0..1..2. .1..2..1..0. .1..2..1..2. .2..0..1..2. .2..0..2..0
..1..2..0..1. .0..1..2..1. .0..2..0..1. .2..0..1..2. .2..0..1..2
..0..2..0..1. .2..1..2..0. .0..1..2..0. .1..2..0..2. .0..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..721

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A000400(n-1).

Column 3 is A055842.

Row 1 is A000079(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)

k=3: a(n) = 5*a(n-1) for n>2

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

k=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3) for n>4

k=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>6

k=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>7

Empirical for row n:

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

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

n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>5

n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>9

n=5: [order 8] for n>12

n=6: [order 13] for n>18

n=7: [order 21] for n>27