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

Author

R. H. Hardin, Jun 08 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n+1)

Column 2 is A024537(n+1)

Column 3 is A094286(n+2)

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]