A269678 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo k+1.

2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 66, 14, 7, 36, 120, 224, 174, 22, 8, 49, 210, 570, 820, 462, 30, 9, 64, 336, 1212, 2670, 2976, 1206, 46, 10, 81, 504, 2282, 6918, 12390, 10700, 3150, 62, 11, 100, 720, 3936, 15358, 39156, 57030, 38224, 8166, 94, 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

..6....24.....60.....120......210.......336.......504........720........990

.10....66....224.....570.....1212......2282......3936.......6354.......9740

.14...174....820....2670.....6918.....15358.....30504......55710......95290

.22...462...2976...12390....39156....102606....234912.....485766.....927780

.30..1206..10700...57030...220050....681254...1799256....4215510....8995310

.46..3150..38224..260790..1229292...4499278..13716480...36430614...86891980

.62..8166.135780.1185990..6832518..29579382.104139336..313684470..836599530

.94.21150.480176.5368470.37810116.193688894.787814400.2692218006.8031245540

Links

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

Formula

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) -a(n-2) -15*a(n-3)

k=4: a(n) = 7*a(n-1) -6*a(n-2) -24*a(n-3)

k=5: a(n) = 9*a(n-1) -13*a(n-2) -35*a(n-3)

k=6: a(n) = 11*a(n-1) -22*a(n-2) -48*a(n-3)

k=7: a(n) = 13*a(n-1) -33*a(n-2) -63*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 + 3*n^2 + 2*n + 2 for n>1

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

n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 + 6*n^2 + 6 for n>1

n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 + 8*n^3 + 10*n^2 + 12*n - 10 for n>1

Example

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

Crossrefs

Column 1 is A027383.

Column 2 is A269461.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A007531(n+2).

Sequence in context: A269409 A268944 A269537 * A269467 A228461 A267471

Adjacent sequences: A269675 A269676 A269677 * A269679 A269680 A269681

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 03 2016

Status

approved