A269606 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.

2, 3, 4, 4, 9, 6, 5, 16, 24, 8, 6, 25, 60, 62, 10, 7, 36, 120, 222, 154, 12, 8, 49, 210, 572, 804, 376, 14, 9, 64, 336, 1220, 2692, 2878, 902, 16, 10, 81, 504, 2298, 7030, 12570, 10192, 2142, 18, 11, 100, 720, 3962, 15630, 40288, 58280, 35812, 5040, 20, 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

..8....62....222.....572.....1220......2298......3962.......6392.......9792

.10...154....804....2692.....7030.....15630.....31024......56584......96642

.12...376...2878...12570....40288....105892....242226.....499798.....952180

.14...902..10192...58280...229754....714874...1886252....4405772....9366790

.16..2142..35812..268704..1304934...4811578..14654952...38768412...92013754

.18..5040.125012.1233046..7385898..32300252.113629480..340600002..902743646

.20.11786.434110.5636046.41679780.216337084.879470154.2988094770.8846649136

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-2)

k=2: a(n) = 5*a(n-1) -5*a(n-2) -8*a(n-3) +12*a(n-4)

k=3: a(n) = 7*a(n-1) -9*a(n-2) -23*a(n-3) +31*a(n-4) +33*a(n-5)

k=4: [order 7]

k=5: [order 7]

k=6: [order 9]

k=7: [order 9]

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 - 4*n^2 + n

n=6: a(n) = n^6 + 6*n^5 + 11*n^4 - 8*n^3 + n^2 + 3*n - 2

n=7: a(n) = n^7 + 7*n^6 + 16*n^5 - 12*n^4 - 5*n^3 + 18*n^2 - 15*n + 4

Example

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

Crossrefs

Column 1 is A004275(n+1).

Column 3 is A269532.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A007531(n+2).

Sequence in context: A097093 A056877 A267232 * A269640 A269409 A268944

Adjacent sequences: A269603 A269604 A269605 * A269607 A269608 A269609

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2016

Status

approved