A212829 T(n,k)=Number of 0..k arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..k order

1, 1, 2, 1, 2, 4, 1, 2, 5, 6, 1, 2, 5, 12, 10, 1, 2, 5, 13, 33, 16, 1, 2, 5, 13, 43, 90, 26, 1, 2, 5, 13, 44, 152, 246, 42, 1, 2, 5, 13, 44, 167, 559, 672, 68, 1, 2, 5, 13, 44, 168, 695, 2091, 1836, 110, 1, 2, 5, 13, 44, 168, 716, 3070, 7882, 5016, 178, 1, 2, 5, 13, 44, 168, 717

Offset

1,3

Comments

Table starts

...1.....1......1.......1.......1.......1.......1.......1.......1.......1

...2.....2......2.......2.......2.......2.......2.......2.......2.......2

...4.....5......5.......5.......5.......5.......5.......5.......5.......5

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

..10....33.....43......44......44......44......44......44......44......44

..16....90....152.....167.....168.....168.....168.....168.....168.....168

..26...246....559.....695.....716.....717.....717.....717.....717.....717

..42...672...2091....3070....3331....3359....3360....3360....3360....3360

..68..1836...7882...14074...16599...17055...17091...17092...17092...17092

.110..5016..29809...65958...87059...92749...93492...93537...93538...93538

.178.13704.112895..313098..473569..534071..545670..546817..546872..546873

.288.37440.427824.1497216.2641428.3220152.3372738.3394616.3396312.3396378

Links

R. H. Hardin, Table of n, a(n) for n = 1..6054

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) +2*a(n-2) for n>5

k=3: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4) for n>7

k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3) +10*a(n-4) +24*a(n-5) +8*a(n-6) for n>9

k=5: a(n) = 11*a(n-1) -30*a(n-2) -21*a(n-3) +112*a(n-4) +63*a(n-5) -119*a(n-6) -120*a(n-7) -30*a(n-8) for n>11

Example

Some solutions for n=8 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....1....1....0....1....1....1....0....1....1....1....1....1
..1....2....2....2....2....1....1....2....2....2....0....2....2....0....2....0
..0....3....3....2....1....0....2....3....1....0....1....3....1....2....3....2
..0....4....3....1....3....2....3....1....0....1....2....0....0....1....4....2
..1....3....2....1....4....0....1....3....3....3....0....2....0....0....0....2
..2....3....1....3....2....1....0....2....3....4....1....2....3....0....0....3
..1....1....4....0....0....2....3....4....1....1....0....2....4....3....4....3

Crossrefs

Column 1 is A128588

Sequence in context: A074634 A152036 A035015 * A210215 A203647 A114791

Adjacent sequences: A212826 A212827 A212828 * A212830 A212831 A212832

Keyword

nonn,tabl

Author

R. H. Hardin May 28 2012

Status

approved