A242549 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..k introduced in 0..k order.

6, 12, 9, 13, 32, 15, 13, 42, 88, 25, 13, 43, 150, 242, 40, 13, 43, 165, 554, 660, 64, 13, 43, 166, 690, 2072, 1800, 104, 13, 43, 166, 711, 3050, 7808, 4920, 169, 13, 43, 166, 712, 3311, 13988, 29536, 13448, 273, 13, 43, 166, 712, 3339, 16512, 65588, 111878, 36736

Offset: 1

Author

R. H. Hardin, May 17 2014

Keywords

• nonn
• tabl

Comments

Table starts

...6.....12......13......13.......13.......13.......13.......13.......13

...9.....32......42......43.......43.......43.......43.......43.......43

..15.....88.....150.....165......166......166......166......166......166

..25....242.....554.....690......711......712......712......712......712

..40....660....2072....3050.....3311.....3339.....3340.....3340.....3340

..64...1800....7808...13988....16512....16968....17004....17005....17005

.104...4920...29536...65588....86671....92360....93103....93148....93149

.169..13448..111878..311431...471698...532175...543773...544920...544975

.273..36736..423969.1489435..2631790..3210136..3362689..3384566..3386262

.441.100352.1607058.7152787.14930915.20066475.21854355.22202698.22241481

Examples

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

Links

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

Crossrefs

Column 1 is A006498(n+4)

Formula

Empirical for column k:

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

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

k=3: [order 8]

k=4: [order 12]

k=5: [order 16]

k=6: [order 20]

k=7: [order 24]