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

1,3

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

Links

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

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

Example

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

Crossrefs

Column 1 is A007051(n-1).

Column 2 is A000400(n-1).

Column 3 is A055842.

Row 1 is A000079(n-2).

Sequence in context: A181661 A144160 A368228 * A200226 A300628 A115255

Adjacent sequences: A275139 A275140 A275141 * A275143 A275144 A275145

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 17 2016

Status

approved