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A243729 T(n,k)=Number of length n+2 0..k arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..k introduced in 0..k order 9
3, 3, 5, 3, 6, 8, 3, 6, 12, 13, 3, 6, 12, 24, 21, 3, 6, 12, 25, 48, 34, 3, 6, 12, 25, 53, 96, 55, 3, 6, 12, 25, 53, 115, 192, 89, 3, 6, 12, 25, 53, 116, 253, 384, 144, 3, 6, 12, 25, 53, 116, 259, 564, 768, 233, 3, 6, 12, 25, 53, 116, 259, 593, 1268, 1536, 377, 3, 6, 12, 25, 53, 116, 259 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
...3....3....3....3....3....3....3....3....3....3....3....3....3....3....3....3
...5....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6
...8...12...12...12...12...12...12...12...12...12...12...12...12...12...12...12
..13...24...25...25...25...25...25...25...25...25...25...25...25...25...25...25
..21...48...53...53...53...53...53...53...53...53...53...53...53...53...53...53
..34...96..115..116..116..116..116..116..116..116..116..116..116..116..116..116
..55..192..253..259..259..259..259..259..259..259..259..259..259..259..259..259
..89..384..564..593..594..594..594..594..594..594..594..594..594..594..594..594
.144..768.1268.1382.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389.1389
.233.1536.2871.3281.3322.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323.3323
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1)
k=3: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -3*a(n-4)
k=4: a(n) = 4*a(n-1) -13*a(n-3) +6*a(n-4) +8*a(n-5)
k=5: a(n) = 5*a(n-1) -29*a(n-3) +20*a(n-4) +51*a(n-5) -31*a(n-6) -30*a(n-7)
k=6: [order 9]
k=7: [order 11]
k=8: [order 13]
k=9: [order 15]
EXAMPLE
Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....1....1....1....1....1....1....1....1....0....1....0
..1....1....1....1....1....1....0....0....1....1....1....1....0....1....0....1
..1....1....0....0....0....2....1....1....2....2....2....2....0....0....1....1
..0....2....1....1....0....2....0....1....2....2....2....1....2....1....0....0
..0....2....1....0....2....3....1....2....0....3....1....2....2....0....0....1
..1....3....2....1....2....3....1....1....0....2....1....2....3....0....2....1
..0....2....1....1....0....0....0....2....1....3....2....0....3....2....0....2
CROSSREFS
Column 1 is A000045(n+3)
Column 2 is A003945
Sequence in context: A057662 A015971 A163167 * A200810 A365710 A114003
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 09 2014
STATUS
approved

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Last modified February 25 11:24 EST 2024. Contains 370325 sequences. (Running on oeis4.)