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A269583
T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by more than one.
11
2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 64, 79, 32, 7, 36, 125, 250, 229, 64, 8, 49, 216, 613, 964, 659, 128, 9, 64, 343, 1276, 2969, 3680, 1889, 256, 10, 81, 512, 2371, 7456, 14239, 13946, 5401, 512, 11, 100, 729, 4054, 16237, 43184, 67763, 52562, 15419, 1024, 12
OFFSET
1,1
COMMENTS
Table starts
....2.....3......4.......5........6.........7.........8..........9.........10
....4.....9.....16......25.......36........49........64.........81........100
....8....27.....64.....125......216.......343.......512........729.......1000
...16....79....250.....613.....1276......2371......4054.......6505.......9928
...32...229....964....2969.....7456.....16237.....31844......57649......97984
...64...659...3680...14239....43184....110339....248464.....507935.....962144
..128..1889..13946...67763...248324....745013...1927694....4453031....9406088
..256..5401..52562..320495..1419502...5003189..14883506...38870827...91601150
..512.15419.197288.1508267..8074172..33444515.114432704..338024963..889023812
.1024.43977.738190.7069055.45734140.222678103.876609410.2929722175.8602245520
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) +a(n-4)
k=3: a(n) = 9*a(n-1) -24*a(n-2) +9*a(n-3) +26*a(n-4) +3*a(n-5)
k=4: a(n) = 16*a(n-1) -93*a(n-2) +220*a(n-3) -112*a(n-4) -192*a(n-5) -2*a(n-6) +8*a(n-7)
k=5: [order 7]
k=6: [order 9]
k=7: [order 9]
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 + 3*n + 1
n=4: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n + 1
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 6*n + 1
n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 15*n^2 + 12*n - 1
n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 28*n^3 + 42*n^2 + 5*n - 1
EXAMPLE
Some solutions for n=6 k=4
..4. .1. .1. .4. .0. .0. .4. .3. .1. .4. .3. .0. .4. .3. .1. .0
..4. .2. .0. .2. .0. .2. .3. .3. .2. .3. .1. .1. .2. .0. .3. .2
..2. .3. .1. .4. .1. .1. .3. .1. .4. .4. .3. .1. .4. .0. .3. .0
..3. .3. .2. .1. .3. .0. .4. .0. .0. .3. .0. .3. .0. .3. .4. .2
..4. .2. .2. .4. .0. .0. .1. .1. .0. .0. .0. .1. .3. .0. .2. .4
..1. .4. .3. .1. .0. .1. .2. .4. .0. .1. .3. .2. .1. .2. .3. .4
CROSSREFS
Column 1 is A000079.
Column 3 is A269489.
Row 1 is A000027(n+1).
Row 2 is A000290(n+1).
Row 3 is A000578(n+1).
Sequence in context: A223949 A224133 A228740 * A250361 A375379 A118263
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 01 2016
STATUS
approved