A269537 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than one.

2, 3, 4, 4, 9, 6, 5, 16, 24, 10, 6, 25, 60, 64, 14, 7, 36, 120, 222, 164, 22, 8, 49, 210, 568, 804, 418, 30, 9, 64, 336, 1210, 2648, 2878, 1048, 46, 10, 81, 504, 2280, 6890, 12214, 10192, 2614, 62, 11, 100, 720, 3934, 15324, 38878, 55836, 35812, 6468, 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....64....222.....568.....1210......2280......3934.......6352.......9738

.14...164....804....2648.....6890.....15324.....30464......55664......95238

.22...418...2878...12214....38878....102202....234358.....485038.....926854

.30..1048..10192...55836...217714....677200...1792788....4205812....8981446

.46..2614..35812..253418..1211476...4462414..13648124...36313762...86704348

.62..6468.125012.1143256..6705102..29265308.103462888..312366672..834223586

.94.15942.434110.5131592.36939610.191134204.781425950.2678039200.8002547722

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) = 4*a(n-1) -a(n-2) -10*a(n-3) +6*a(n-4) +4*a(n-5)

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: a(n) = 14*a(n-1) -65*a(n-2) +80*a(n-3) +163*a(n-4) -280*a(n-5) -208*a(n-6)

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 + 3*n^2 + 2*n

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

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

n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 12*n^3 + 22*n^2 - 18*n + 4

Example

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

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: A269640 A269409 A268944 * A269678 A269467 A228461

Adjacent sequences: A269534 A269535 A269536 * A269538 A269539 A269540

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 29 2016

Status

approved