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

Offset: 1

Author

R. H. Hardin, May 15 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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)

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]