A243607 T(n,k) = Number of length n+2 0..k arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..k introduced in 0..k order.

3, 4, 5, 4, 9, 8, 4, 10, 21, 13, 4, 10, 28, 50, 21, 4, 10, 29, 85, 120, 34, 4, 10, 29, 96, 269, 289, 55, 4, 10, 29, 97, 349, 870, 697, 89, 4, 10, 29, 97, 365, 1350, 2844, 1682, 144, 4, 10, 29, 97, 366, 1511, 5425, 9346, 4060, 233, 4, 10, 29, 97, 366, 1533, 6726, 22297, 30792

Offset

1,1

Comments

Table starts

...3....4......4......4......4......4.......4.......4.......4.......4.......4

...5....9.....10.....10.....10.....10......10......10......10......10......10

...8...21.....28.....29.....29.....29......29......29......29......29......29

..13...50.....85.....96.....97.....97......97......97......97......97......97

..21..120....269....349....365....366.....366.....366.....366.....366.....366

..34..289....870...1350...1511...1533....1534....1534....1534....1534....1534

..55..697...2844...5425...6726...7020....7049....7050....7050....7050....7050

..89.1682...9346..22297..31544..34631...35129...35166...35167...35167...35167

.144.4060..30792..92841.153328.181391..187993..188788..188834..188835..188835

.233.9801.101577.389456.763187.995139.1069914.1082913.1084123.1084179.1084180

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) = 3*a(n-1) -a(n-2) -a(n-3),

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

k=4: a(n) = 8*a(n-1) -18*a(n-2) +5*a(n-3) +17*a(n-4) -4*a(n-5) -6*a(n-6) -a(n-7),

k=5: [order 9],

k=6: [order 11],

k=7: [order 13],

k=8: [order 15],

k=9: [order 17].

Example

Some solutions for n=5, k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....0....1....1....0....0....1....1....1....1....1....0....1
..1....1....1....1....1....2....2....0....0....2....2....2....2....2....0....1
..2....0....1....2....2....3....3....0....1....3....2....3....2....2....1....1
..2....2....1....3....3....1....0....1....2....0....3....4....1....1....2....1
..3....3....0....1....3....1....4....1....2....0....3....0....3....3....2....1
..4....1....2....1....0....0....3....0....0....2....3....1....0....3....1....0

Crossrefs

Column 1 is A000045(n+3).

Column 2 is A024537(n+1).

Sequence in context: A178698 A225072 A262906 * A242472 A272895 A319460

Adjacent sequences: A243604 A243605 A243606 * A243608 A243609 A243610

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 07 2014

Status

approved