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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

Views

Author

R. H. Hardin, May 15 2014

Keywords

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

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]
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