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

Author

R. H. Hardin, Mar 01 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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).

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