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

Author

R. H. Hardin, Jun 07 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000045(n+3).

Column 2 is A024537(n+1).

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].