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.

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

R. H. Hardin, Table of n, a(n) for n = 1..9999

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 A202784 A118263

Adjacent sequences: A269580 A269581 A269582 * A269584 A269585 A269586

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2016

Status

approved