A269776 T(n,k)=Number of length-n 0..k arrays with every repeated value unequal to the previous repeated value plus one mod k+1.

2, 3, 4, 4, 9, 8, 5, 16, 27, 14, 6, 25, 64, 78, 24, 7, 36, 125, 252, 222, 40, 8, 49, 216, 620, 984, 624, 66, 9, 64, 343, 1290, 3060, 3816, 1740, 108, 10, 81, 512, 2394, 7680, 15040, 14724, 4824, 176, 11, 100, 729, 4088, 16674, 45600, 73680, 56592, 13320, 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....78....252.....620.....1290......2394.......4088.......6552.......9990

..24...222....984....3060.....7680.....16674......32592......58824......99720

..40...624...3816...15040....45600....115920.....259504.....527616.....994680

..66..1740..14724...73680...270150....804636....2063880....4728384....9915210

.108..4824..56592..360000..1597500...5577768...16398144...42342912...98779500

.176.13320.216864.1755200..9432000..38621016..130175360..378929664..983566800

.286.36672.829116.8542720.55616250.267152256.1032602872.3389054976.9788946390

Links

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

Formula

Empirical for column k (apparently a(n) = 2*k*a(n-1) -k*(k-1)*a(n-2) -k^2*a(n-3)):

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

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

k=3: a(n) = 6*a(n-1) -6*a(n-2) -9*a(n-3)

k=4: a(n) = 8*a(n-1) -12*a(n-2) -16*a(n-3)

k=5: a(n) = 10*a(n-1) -20*a(n-2) -25*a(n-3)

k=6: a(n) = 12*a(n-1) -30*a(n-2) -36*a(n-3)

k=7: a(n) = 14*a(n-1) -42*a(n-2) -49*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 + 3*n

n=5: a(n) = n^5 + 5*n^4 + 10*n^3 + 7*n^2 + n

n=6: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 4*n^2

n=7: a(n) = n^7 + 7*n^6 + 21*n^5 + 25*n^4 + 11*n^3 + n^2

Example

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

Crossrefs

Column 1 is A019274(n+2).

Column 2 is A269613.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A000578(n+1).

Row 4 is A058895(n+1).

Sequence in context: A250351 A269690 A269494 * A269619 A269435 A269656

Adjacent sequences: A269773 A269774 A269775 * A269777 A269778 A269779

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 04 2016

Status

approved