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

Author

R. H. Hardin, Jul 03 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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).

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