A268944 T(n,k)=Number of length-n 0..k arrays with no repeated value unequal to the previous repeated value plus one mod k+1.

2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 63, 14, 7, 36, 120, 220, 159, 22, 8, 49, 210, 565, 788, 396, 30, 9, 64, 336, 1206, 2615, 2780, 969, 46, 10, 81, 504, 2275, 6834, 11950, 9684, 2349, 62, 11, 100, 720, 3928, 15239, 38322, 54045, 33404, 5640, 94, 12, 121, 990

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....63....220.....565.....1206......2275......3928.......6345.......9730

.14...159....788....2615.....6834.....15239.....30344......55503......95030

.22...396...2780...11950....38322....101192....232696.....482490.....923150

.30...969...9684...54045...213042....667065...1773384....4171869....8925990

.46..2349..33404..242365..1175850...4370261..13443064...35904789...85953830

.62..5640.114292.1079240..6450402..28480312.101433800..307754712..824720230

.94.13455.388444.4777225.35200458.184750699.762265720.2628421029.7887767350

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) +a(n-2) -6*a(n-3)

k=3: a(n) = 5*a(n-1) -2*a(n-2) -12*a(n-3)

k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3)

k=5: a(n) = 9*a(n-1) -14*a(n-2) -30*a(n-3)

k=6: a(n) = 11*a(n-1) -23*a(n-2) -42*a(n-3)

k=7: a(n) = 13*a(n-1) -34*a(n-2) -56*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 + n + 1

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

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

n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 10*n^4 + 4*n^3 + n^2 + 4*n - 3

Example

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

Crossrefs

Column 1 is A027383.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A007531(n+2).

Sequence in context: A269606 A269640 A269409 * A269537 A269678 A269467

Adjacent sequences: A268941 A268942 A268943 * A268945 A268946 A268947

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2016

Status

approved