A243033 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..k introduced in 0..k order

6, 12, 9, 13, 32, 13, 13, 42, 85, 19, 13, 43, 147, 226, 28, 13, 43, 162, 536, 601, 41, 13, 43, 163, 672, 1987, 1598, 60, 13, 43, 163, 693, 2962, 7414, 4249, 88, 13, 43, 163, 694, 3223, 13540, 27736, 11298, 129, 13, 43, 163, 694, 3251, 16060, 63221, 103868, 30041, 189

Offset

1,1

Comments

Table starts

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

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

..13....85.....147.....162......163......163......163......163......163

..19...226.....536.....672......693......694......694......694......694

..28...601....1987....2962.....3223.....3251.....3252.....3252.....3252

..41..1598....7414...13540....16060....16516....16552....16553....16553

..60..4249...27736...63221....84207....89891....90634....90679....90680

..88.11298..103868..298775...457676...517995...529587...530734...530789

.129.30041..389129.1421589..2549156..3124633..3276946..3298816..3300512

.189.79878.1458054.6789700.14430921.19526936.21309360.21657357.21696132

Links

R. H. Hardin, Table of n, a(n) for n = 1..6280

Formula

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) -a(n-2) +2*a(n-3) -6*a(n-4) -2*a(n-5) -3*a(n-6)

k=4: [order 9]

k=5: [order 12]

k=6: [order 15]

k=7: [order 18]

Example

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

Crossrefs

Column 1 is A000930(n+5)

Sequence in context: A292680 A028320 A119437 * A242549 A315777 A372453

Adjacent sequences: A243030 A243031 A243032 * A243034 A243035 A243036

Keyword

nonn,tabl

Author

R. H. Hardin, May 29 2014

Status

approved