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A269467
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T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value.
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12
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2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 66, 14, 7, 36, 120, 228, 174, 22, 8, 49, 210, 580, 852, 462, 30, 9, 64, 336, 1230, 2780, 3180, 1206, 46, 10, 81, 504, 2310, 7170, 13300, 11796, 3150, 62, 11, 100, 720, 3976, 15834, 41730, 63420, 43644, 8166, 94, 12, 121
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OFFSET
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1,1
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COMMENTS
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Table starts
..2.....3......4.......5........6.........7.........8..........9.........10
..4.....9.....16......25.......36........49........64.........81........100
..6....24.....60.....120......210.......336.......504........720........990
.10....66....228.....580.....1230......2310......3976.......6408.......9810
.14...174....852....2780.....7170.....15834.....31304......56952......97110
.22...462...3180...13300....41730....108402....246232.....505800.....960750
.30..1206..11796...63420...242370....741090...1934856....4488696....9499590
.46..3150..43644..301780..1405530...5060706..15190840...39808584...93880710
.62..8166.160980.1433180..8139570..34523202.119174216..352838520..927352710
.94.21150.592572.6795700.47082330.235304034.934305400.3125681352.9156504150
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3)
k=3: a(n) = 5*a(n-1) -18*a(n-3)
k=4: a(n) = 7*a(n-1) -4*a(n-2) -32*a(n-3)
k=5: a(n) = 9*a(n-1) -10*a(n-2) -50*a(n-3)
k=6: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3)
k=7: a(n) = 13*a(n-1) -28*a(n-2) -98*a(n-3)
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 2*n
n=4: a(n) = n^4 + 4*n^3 + 4*n^2 + n
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 2*n^2 - n
n=6: a(n) = n^6 + 6*n^5 + 11*n^4 + 4*n^3 - n^2 + n
n=7: a(n) = n^7 + 7*n^6 + 16*n^5 + 8*n^4 - n^3 - n
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EXAMPLE
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Some solutions for n=6 k=4
..2. .0. .3. .1. .1. .1. .2. .0. .1. .0. .3. .0. .3. .2. .4. .1
..4. .3. .1. .1. .2. .0. .0. .2. .0. .2. .3. .1. .4. .0. .3. .4
..3. .2. .0. .0. .0. .0. .2. .2. .1. .0. .4. .2. .4. .0. .4. .3
..3. .0. .4. .2. .1. .1. .2. .1. .3. .4. .1. .4. .2. .4. .4. .1
..1. .3. .4. .4. .0. .4. .4. .3. .4. .1. .4. .1. .2. .2. .0. .0
..0. .1. .3. .3. .4. .3. .2. .4. .1. .3. .2. .2. .1. .4. .1. .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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