A269690 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by plus or minus one modulo k+1.

2, 3, 4, 4, 9, 8, 5, 16, 27, 14, 6, 25, 64, 75, 24, 7, 36, 125, 248, 201, 40, 8, 49, 216, 615, 944, 525, 66, 9, 64, 343, 1284, 2995, 3544, 1347, 108, 10, 81, 512, 2387, 7584, 14465, 13168, 3411, 176, 11, 100, 729, 4080, 16541, 44556, 69405, 48536, 8553, 286, 12, 121

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

..14....75....248.....615.....1284......2387......4080.......6543.......9980

..24...201....944....2995.....7584.....16541.....32416......58599......99440

..40...525...3544...14465....44556....114205....256880.....523809.....989380

..66..1347..13168...69405...260616....786079...2031072....4674393....9831160

.108..3411..48536..331255..1518804...5396363..16027696...41651631...97576460

.176..8553.177776.1574195..8823984..36961757.126262688..370652391..967466240

.286.21285.647896.7454385.51132636.252671461.993181680.3294529281.9583467220

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) -a(n-3)

k=2: a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3)

k=3: a(n) = 6*a(n-1) -7*a(n-2) -6*a(n-3)

k=4: a(n) = 8*a(n-1) -13*a(n-2) -12*a(n-3)

k=5: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3)

k=6: a(n) = 12*a(n-1) -31*a(n-2) -30*a(n-3)

k=7: a(n) = 14*a(n-1) -43*a(n-2) -42*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 + 3*n + 1

n=4: a(n) = n^4 + 4*n^3 + 6*n^2 + 2*n - 1 for n>1

n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 - 3*n - 1 for n>1

n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 - 7*n^2 - 4*n + 1 for n>1

n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 - 13*n^3 - 11*n^2 + 3*n + 1 for n>1

Example

Some solutions for n=6 k=4
..0. .3. .4. .2. .4. .3. .3. .0. .3. .0. .4. .1. .1. .3. .0. .0
..1. .2. .1. .2. .0. .0. .0. .4. .0. .1. .1. .3. .3. .2. .2. .2
..3. .3. .0. .4. .2. .2. .2. .4. .0. .0. .2. .3. .1. .1. .1. .2
..2. .1. .0. .3. .2. .0. .2. .3. .0. .3. .0. .4. .3. .0. .3. .4
..4. .0. .3. .4. .4. .1. .4. .4. .3. .2. .3. .0. .3. .2. .3. .1
..4. .2. .1. .3. .0. .4. .2. .3. .2. .2. .1. .1. .1. .1. .3. .0

Crossrefs

Column 1 is A019274(n+2).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A000578(n+1).

Row 4 is A246767(n+2) for n>1.

Sequence in context: A244940 A244832 A250351 * A269494 A269776 A269619

Adjacent sequences: A269687 A269688 A269689 * A269691 A269692 A269693

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 03 2016

Status

approved