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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
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 08 2014
STATUS
approved