A269467 T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value.

2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 66, 14, 7, 36, 120, 228, 174, 22, 8, 49, 210, 580, 852, 462, 30, 9, 64, 336, 1230, 2780, 3180, 1206, 46, 10, 81, 504, 2310, 7170, 13300, 11796, 3150, 62, 11, 100, 720, 3976, 15834, 41730, 63420, 43644, 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....228.....580.....1230......2310......3976.......6408.......9810

.14...174....852....2780.....7170.....15834.....31304......56952......97110

.22...462...3180...13300....41730....108402....246232.....505800.....960750

.30..1206..11796...63420...242370....741090...1934856....4488696....9499590

.46..3150..43644..301780..1405530...5060706..15190840...39808584...93880710

.62..8166.160980.1433180..8139570..34523202.119174216..352838520..927352710

.94.21150.592572.6795700.47082330.235304034.934305400.3125681352.9156504150

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) -18*a(n-3)

k=4: a(n) = 7*a(n-1) -4*a(n-2) -32*a(n-3)

k=5: a(n) = 9*a(n-1) -10*a(n-2) -50*a(n-3)

k=6: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3)

k=7: a(n) = 13*a(n-1) -28*a(n-2) -98*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 + 4*n^2 + n

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

n=6: a(n) = n^6 + 6*n^5 + 11*n^4 + 4*n^3 - n^2 + n

n=7: a(n) = n^7 + 7*n^6 + 16*n^5 + 8*n^4 - n^3 - n

Example

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

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: A268944 A269537 A269678 * A228461 A267471 A268457

Adjacent sequences: A269464 A269465 A269466 * A269468 A269469 A269470

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 27 2016

Status

approved