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

Author

R. H. Hardin, Feb 29 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

.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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A027383.

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) = 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