A243641 T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and new values 0..k introduced in 0..k order

4, 4, 8, 4, 9, 16, 4, 9, 21, 32, 4, 9, 21, 50, 64, 4, 9, 21, 51, 120, 128, 4, 9, 21, 51, 127, 289, 256, 4, 9, 21, 51, 127, 323, 697, 512, 4, 9, 21, 51, 127, 324, 835, 1682, 1024, 4, 9, 21, 51, 127, 324, 844, 2187, 4060, 2048, 4, 9, 21, 51, 127, 324, 844, 2242, 5787, 9801, 4096, 4

Offset

1,1

Comments

Table starts

....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4

....8....9.....9.....9.....9.....9.....9.....9.....9.....9.....9.....9.....9

...16...21....21....21....21....21....21....21....21....21....21....21....21

...32...50....51....51....51....51....51....51....51....51....51....51....51

...64..120...127...127...127...127...127...127...127...127...127...127...127

..128..289...323...324...324...324...324...324...324...324...324...324...324

..256..697...835...844...844...844...844...844...844...844...844...844...844

..512.1682..2187..2242..2243..2243..2243..2243..2243..2243..2243..2243..2243

.1024.4060..5787..6062..6073..6073..6073..6073..6073..6073..6073..6073..6073

.2048.9801.15435.16655.16736.16737.16737.16737.16737.16737.16737.16737.16737

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -6*a(n-2) -2*a(n-3) +4*a(n-4)

k=4: a(n) = 7*a(n-1) -14*a(n-2) +21*a(n-4) -7*a(n-5) -6*a(n-6)

k=5: [order 8]

k=6: [order 10]

k=7: [order 12]

k=8: [order 14]

k=9: [order 16]

Example

Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....0....0....1....1....0....0....0....0....1....1....0....1....1....0
..1....1....1....0....1....0....0....0....1....1....1....0....0....1....1....1
..1....1....0....1....1....0....1....0....0....1....2....0....1....2....2....1
..2....2....0....0....0....0....0....0....0....2....1....1....1....2....2....0
..2....1....1....1....1....1....0....0....0....1....1....1....0....1....3....1
..3....1....1....1....0....0....0....0....1....1....1....1....0....1....3....1
..2....2....1....1....1....1....0....1....1....1....0....0....2....2....0....0

Crossrefs

Column 1 is A000079(n+1)

Column 2 is A024537(n+1)

Column 3 is A094286(n+2)

Sequence in context: A273765 A273854 A082075 * A276620 A276681 A255485

Adjacent sequences: A243638 A243639 A243640 * A243642 A243643 A243644

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 08 2014

Status

approved