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

1,1

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

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-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]

Example

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

Crossrefs

Column 1 is A006498(n+4)

Sequence in context: A028320 A119437 A243033 * A315777 A378930 A372453

Adjacent sequences: A242546 A242547 A242548 * A242550 A242551 A242552

Keyword

nonn,tabl

Author

R. H. Hardin, May 17 2014

Status

approved