A274728 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) or (-1,0) and new values introduced in order 0..2.

1, 2, 1, 5, 6, 2, 14, 24, 16, 4, 41, 96, 68, 48, 8, 122, 384, 296, 260, 144, 16, 365, 1536, 1300, 1632, 1040, 432, 32, 1094, 6144, 5728, 10368, 9308, 4132, 1296, 64, 3281, 24576, 25268, 66132, 84948, 52912, 16524, 3888, 128, 9842, 98304, 111512, 421904, 771300

Offset

1,2

Comments

Table starts

...1.....2.......5.......14.........41..........122...........365

...1.....6......24.......96........384.........1536..........6144

...2....16......68......296.......1300.........5728.........25268

...4....48.....260.....1632......10368........66132........421904

...8...144....1040.....9308......84948.......771300.......7016284

..16...432....4132....52912.....687248......8960464.....116633012

..32..1296...16524...301784....5634776....105328812....1980677448

..64..3888...66088..1721528...45990340...1237030912...33415073716

.128.11664..264332..9816048..375845052..14505195904..564905405336

.256.34992.1057316.55981988.3070055916.170291855288.9541460598408

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

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

k=4: [order 8] for n>12

k=5: [order 15] for n>19

k=6: [order 30] for n>35

k=7: [order 59] for n>65

Empirical for row n:

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

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

n=3: a(n) = 6*a(n-1) -7*a(n-2) for n>3

n=4: a(n) = 8*a(n-1) -10*a(n-2) -4*a(n-3) +13*a(n-4) -7*a(n-5) +a(n-6) for n>7

n=5: [order 7] for n>9

n=6: [order 18] for n>20

n=7: [order 30] for n>34

Example

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

Crossrefs

Column 1 is A000079(n-2).

Row 1 is A007051(n-1).

Row 2 is A002023(n-2).

Row 3 is A235643(n-1).

Sequence in context: A209170 A231732 A185384 * A062991 A234950 A275228

Adjacent sequences: A274725 A274726 A274727 * A274729 A274730 A274731

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 03 2016

Status

approved