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

Author

R. H. Hardin May 28 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A128588

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