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A242472 T(n,k)=Number of length n+2 0..k arrays with no three equal elements in a row and new values 0..k introduced in 0..k order 6
3, 4, 5, 4, 11, 8, 4, 12, 30, 13, 4, 12, 40, 82, 21, 4, 12, 41, 143, 224, 34, 4, 12, 41, 158, 528, 612, 55, 4, 12, 41, 159, 663, 1979, 1672, 89, 4, 12, 41, 159, 684, 2944, 7466, 4568, 144, 4, 12, 41, 159, 685, 3204, 13537, 28246, 12480, 233, 4, 12, 41, 159, 685, 3232 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...3.....4......4.......4.......4.......4.......4.......4.......4.......4

...5....11.....12......12......12......12......12......12......12......12

...8....30.....40......41......41......41......41......41......41......41

..13....82....143.....158.....159.....159.....159.....159.....159.....159

..21...224....528.....663.....684.....685.....685.....685.....685.....685

..34...612...1979....2944....3204....3232....3233....3233....3233....3233

..55..1672...7466...13537...16042...16497...16533...16534...16534...16534

..89..4568..28246...63551...84412...90075...90817...90862...90863...90863

.144.12480.106992..301968..460174..520248..531812..532958..533013..533014

.233.34096.405481.1444795.2570411.3143900.3295779.3317613.3319308.3319374

LINKS

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

FORMULA

Empirical for column k:

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

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

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

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)

k=5: [order 8]

k=6: [order 10]

k=7: [order 12]

k=8: [order 14]

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....0....1....1....1....1....1....1....1....1....0

..0....2....2....1....1....0....1....2....2....2....1....1....2....2....2....1

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

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

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

CROSSREFS

Column 1 is A000045(n+3)

Column 2 is A021006(n-1)

Column 3 is A204678(n+2)

Column 4 is A222919(n+2)

Sequence in context: A225072 A262906 A243607 * A272895 A161386 A085600

Adjacent sequences:  A242469 A242470 A242471 * A242473 A242474 A242475

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 15 2014

STATUS

approved

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Last modified April 27 01:03 EDT 2018. Contains 303149 sequences. (Running on oeis4.)