A268956 T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 4, 11, 7, 1, 2, 4, 12, 29, 11, 1, 2, 4, 12, 39, 77, 15, 1, 2, 4, 12, 40, 138, 201, 23, 1, 2, 4, 12, 40, 153, 499, 525, 31, 1, 2, 4, 12, 40, 154, 634, 1830, 1361, 47, 1, 2, 4, 12, 40, 154, 655, 2785, 6723, 3525, 63, 1, 2, 4, 12, 40, 154, 656, 3045

Offset: 1

Author

R. H. Hardin, Feb 16 2016

Keywords

• nonn
• tabl

Comments

Table starts

..1....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1.....1

..2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2.....2

..3....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4.....4

..5...11....12....12....12....12....12....12....12....12....12....12....12

..7...29....39....40....40....40....40....40....40....40....40....40....40

.11...77...138...153...154...154...154...154...154...154...154...154...154

.15..201...499...634...655...656...656...656...656...656...656...656...656

.23..525..1830..2785..3045..3073..3074..3074..3074..3074..3074..3074..3074

.31.1361..6723.12634.15124.15579.15615.15616.15616.15616.15616.15616.15616

.47.3525.24714.58409.78930.84572.85314.85359.85360.85360.85360.85360.85360

Examples

			Some solutions for n=8 k=4
..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
..1. .1. .1. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1
..2. .2. .2. .1. .2. .2. .0. .1. .1. .2. .2. .2. .2. .0. .2. .2
..2. .3. .2. .0. .3. .3. .2. .2. .2. .1. .2. .3. .1. .1. .0. .1
..1. .4. .3. .2. .4. .2. .1. .3. .3. .3. .3. .1. .0. .2. .0. .3
..1. .3. .4. .1. .4. .2. .3. .0. .3. .3. .3. .4. .2. .1. .3. .4
..2. .2. .0. .2. .3. .4. .0. .1. .1. .1. .2. .0. .0. .2. .1. .2
..0. .0. .0. .3. .1. .1. .3. .2. .4. .3. .1. .0. .0. .1. .0. .2
		

Links

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

Crossrefs

Column 1 is A052955(n-1).

Column 2 is A267912.

Column 3 is A268069.

Diagonal is A268010.

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +2*a(n-2) -8*a(n-3) for n>5

k=3: a(n) = 6*a(n-1) -3*a(n-2) -30*a(n-3) +28*a(n-4) +36*a(n-5) -36*a(n-6) for n>8

k=4: [order 9] for n>11

k=5: [order 12] for n>14

k=6: [order 15] for n>17

k=7: [order 18] for n>20