A242472 - OEIS

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

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 A319460 A343528

Adjacent sequences: A242469 A242470 A242471 * A242473 A242474 A242475

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 15 2014

STATUS

approved