A268069 -id:A268069 - cp's OEIS frontend

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

R. H. Hardin, Feb 16 2016

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

			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

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

Column 1 is A052955(n-1).
Column 2 is A267912.
Column 3 is A268069.
Diagonal is A268010.

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

A268423 T(n,k)=Number of nXk 0..3 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

1, 2, 2, 4, 15, 5, 12, 159, 187, 14, 39, 2191, 9054, 2530, 44, 138, 30295, 494098, 467899, 34195, 147, 499, 421471, 25770278, 92967597, 22309009, 448667, 505, 1830, 5797959, 1339895662, 17282463434, 15615613747, 999810316, 5720450, 1750, 6723, 79367143

Offset: 1

R. H. Hardin, Feb 04 2016

Table starts
....1.........2.............4..............12...............39..............138
....2........15...........159............2191............30295...........421471
....5.......187..........9054..........494098.........25770278.......1339895662
...14......2530........467899........92967597......17282463434....3197637400309
...44.....34195......22309009.....15615613747...10053286458091.6434348326690233
..147....448667.....999810316...2414369699870.5273786308929110
..505...5720450...42764566838.350815694801710
.1750..71224847.1764109373799
.6065.869969995

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

R. H. Hardin, Table of n, a(n) for n = 1..60

Column 3 is A268047.
Row 1 is A268069.
Row 2 is A268070.
Row 3 is A268178.

cp's OEIS Frontend

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.

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