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

1,3

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

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) = 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

Example

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

Crossrefs

Column 1 is A052955(n-1).

Column 2 is A267912.

Column 3 is A268069.

Diagonal is A268010.

Sequence in context: A214314 A209435 A263744 * A208515 A286880 A178030

Adjacent sequences: A268953 A268954 A268955 * A268957 A268958 A268959

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2016

Status

approved