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A255622
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T(n,k)=Number of length n+k 0..2 arrays with at most two downsteps in every k consecutive neighbor pairs
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12
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9, 27, 27, 81, 81, 81, 237, 243, 243, 243, 651, 694, 729, 729, 729, 1647, 1803, 2040, 2187, 2187, 2187, 3834, 4248, 5088, 5997, 6561, 6561, 6561, 8272, 9186, 11386, 14381, 17622, 19683, 19683, 19683, 16698, 18483, 23298, 30816, 40659, 51768, 59049, 59049
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OFFSET
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1,1
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COMMENTS
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Table starts
......9.....27......81.....237.....651.....1647.....3834.....8272....16698
.....27.....81.....243.....694....1803.....4248.....9186....18483....35016
.....81....243.....729....2040....5088....11386....23298....44361....79692
....243....729....2187....5997...14381....30816....60390...110270...190269
....729...2187....6561...17622...40659....83325...156563...275166...458604
...2187...6561...19683...51768..114546...225253...405687...685713..1103630
...6561..19683...59049..152106..322078...602886..1047141..1706242..2653107
..19683..59049..177147..446932..907110..1605726..2656032..4203558..6343974
..59049.177147..531441.1313199.2556858..4293918..6682971.10111362.14922893
.177147.531441.1594323.3858468.7205734.11529741.16925280.24065191.34121019
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 3*a(n-1)
k=3: a(n) = 3*a(n-1)
k=4: a(n) = 3*a(n-1) -a(n-3) +3*a(n-4) -3*a(n-5) -8*a(n-6) +9*a(n-7) -3*a(n-8) +a(n-9)
k=5: [order 14]
k=6: [order 20]
k=7: [order 30]
Empirical for row n:
n=1: [polynomial of degree 8]
n=2: [polynomial of degree 8]
n=3: [polynomial of degree 8]
n=4: [polynomial of degree 8] for n>2
n=5: [polynomial of degree 8] for n>3
n=6: [polynomial of degree 8] for n>4
n=7: [polynomial of degree 8] for n>5
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EXAMPLE
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Some solutions for n=4 k=4
..0....0....0....1....1....1....2....0....0....1....2....2....0....0....1....0
..2....0....0....0....2....2....2....2....1....1....1....0....0....0....1....0
..1....0....2....1....1....0....0....0....2....0....2....2....2....2....1....1
..1....1....1....2....2....2....1....1....2....2....2....1....1....0....1....0
..2....2....0....2....0....0....1....2....0....0....2....2....1....1....0....2
..2....2....0....2....1....0....2....2....1....1....0....1....2....1....1....1
..1....0....1....2....1....2....2....1....2....2....1....2....0....1....2....2
..2....2....0....2....0....1....0....2....0....1....2....1....0....2....2....2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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