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

1,1

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

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) -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

Example

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

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).

Sequence in context: A269690 A269494 A269776 * A269435 A269656 A223949

Adjacent sequences: A269616 A269617 A269618 * A269620 A269621 A269622

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2016

Status

approved