A243729 T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..k introduced in 0..k order

3, 3, 5, 3, 6, 8, 3, 6, 12, 13, 3, 6, 12, 24, 21, 3, 6, 12, 25, 48, 34, 3, 6, 12, 25, 53, 96, 55, 3, 6, 12, 25, 53, 115, 192, 89, 3, 6, 12, 25, 53, 116, 253, 384, 144, 3, 6, 12, 25, 53, 116, 259, 564, 768, 233, 3, 6, 12, 25, 53, 116, 259, 593, 1268, 1536, 377, 3, 6, 12, 25, 53, 116, 259

Offset

1,1

Comments

Table starts

...3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3

...5....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6

...8...12...12...12...12...12...12...12...12...12...12...12...12...12...12...12

..13...24...25...25...25...25...25...25...25...25...25...25...25...25...25...25

..21...48...53...53...53...53...53...53...53...53...53...53...53...53...53...53

..34...96..115..116..116..116..116..116..116..116..116..116..116..116..116..116

..55..192..253..259..259..259..259..259..259..259..259..259..259..259..259..259

..89..384..564..593..594..594..594..594..594..594..594..594..594..594..594..594

.144..768.1268.1382.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389

.233.1536.2871.3281.3322.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323

Links

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

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 4*a(n-1) -13*a(n-3) +6*a(n-4) +8*a(n-5)

k=5: a(n) = 5*a(n-1) -29*a(n-3) +20*a(n-4) +51*a(n-5) -31*a(n-6) -30*a(n-7)

k=6: [order 9]

k=7: [order 11]

k=8: [order 13]

k=9: [order 15]

Example

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

Crossrefs

Column 1 is A000045(n+3)

Column 2 is A003945

Sequence in context: A057662 A015971 A163167 * A200810 A365710 A114003

Adjacent sequences: A243726 A243727 A243728 * A243730 A243731 A243732

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 09 2014

Status

approved