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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 12 19:25 EST 2019. Contains 329078 sequences. (Running on oeis4.)