A242584 T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern aabb (with a!=b) and new values 0..k introduced in 0..k order

7, 13, 12, 14, 35, 21, 14, 45, 97, 37, 14, 46, 159, 271, 65, 14, 46, 174, 587, 757, 114, 14, 46, 175, 723, 2209, 2115, 200, 14, 46, 175, 744, 3192, 8391, 5913, 351, 14, 46, 175, 745, 3453, 14648, 32020, 16535, 616, 14, 46, 175, 745, 3481, 17178, 68819, 122439, 46237

Offset

1,1

Comments

Table starts

....7.....13......14......14.......14.......14.......14.......14.......14

...12.....35......45......46.......46.......46.......46.......46.......46

...21.....97.....159.....174......175......175......175......175......175

...37....271.....587.....723......744......745......745......745......745

...65....757....2209....3192.....3453.....3481.....3482.....3482.....3482

..114...2115....8391...14648....17178....17634....17670....17671....17671

..200...5913...32020...68819....90033....95729....96472....96517....96518

..351..16535..122439..327821...489821...550503...562109...563256...563311

..616..46237..468605.1574161..2734513..3316400..3469255..3491141..3492837

.1081.129291.1794215.7594177.15534111.20716789.22511261.22860029.22898822

Links

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

Formula

Empirical for column k:

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

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

k=3: a(n) = 7*a(n-1) -18*a(n-2) +32*a(n-3) -45*a(n-4) +37*a(n-5) -21*a(n-6) +9*a(n-7)

k=4: [order 10]

k=5: [order 13]

k=6: [order 16]

k=7: [order 19]

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....1....1....1....1....1....1....1....1....1....0....1....1....1....1
..0....2....0....2....2....2....2....2....2....2....2....1....1....2....2....2
..2....1....2....2....3....0....0....3....3....1....3....2....1....1....0....2
..1....2....0....0....4....3....3....0....3....0....4....3....2....3....2....3
..3....3....0....3....1....3....2....4....3....3....3....2....1....3....3....4
..2....2....3....4....2....4....4....3....2....1....3....1....2....0....4....0

Crossrefs

Column 1 is A005251(n+5)

Sequence in context: A259232 A329017 A243389 * A135555 A243044 A229831

Adjacent sequences: A242581 A242582 A242583 * A242585 A242586 A242587

Keyword

nonn,tabl

Author

R. H. Hardin, May 17 2014

Status

approved