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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. 10
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 16 2016
STATUS
approved

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Last modified February 25 13:12 EST 2024. Contains 370330 sequences. (Running on oeis4.)