A269619 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

2, 3, 4, 4, 9, 8, 5, 16, 27, 15, 6, 25, 64, 78, 28, 7, 36, 125, 249, 222, 51, 8, 49, 216, 612, 954, 624, 92, 9, 64, 343, 1275, 2956, 3611, 1740, 164, 10, 81, 512, 2370, 7440, 14125, 13544, 4824, 290, 11, 100, 729, 4053, 16218, 43013, 66925, 50442, 13320, 509, 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

...8....27.....64.....125......216.......343.......512........729.......1000

..15....78....249.....612.....1275......2370......4053.......6504.......9927

..28...222....954....2956.....7440.....16218.....31822......57624......97956

..51...624...3611...14125....43013....110099....248143.....507521.....961625

..92..1740..13544...66925...246798....742487...1923796....4447329....9398090

.164..4824..50442..314935..1407232...4979260..14840928...38800210...91490344

.290.13320.186822.1473779..7982022..33232924.113998742..337209090..887591878

.509.36672.688899.6865098.45074673.220896016.872397577.2920747321.8584628259

Examples

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

Links

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

Crossrefs

Column 1 is A029907(n+1).

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A000578(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = 12*a(n-1) -51*a(n-2) +81*a(n-3) -3*a(n-4) -63*a(n-5) -24*a(n-6) -9*a(n-7)

k=4: [order 7]

k=5: [order 13]

k=6: [order 15]

k=7: [order 17]

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 + 3*n + 1

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

n=5: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 3*n

n=6: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2

n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + 35*n^4 + 18*n^3 + 36*n^2 - 19*n - 7 for n>2