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A269409 T(n,k)=Number of length-n 0..k arrays with no repeated value greater than or equal to the previous repeated value. 9
2, 3, 4, 4, 9, 6, 5, 16, 24, 9, 6, 25, 60, 63, 12, 7, 36, 120, 222, 159, 16, 8, 49, 210, 570, 804, 394, 20, 9, 64, 336, 1215, 2670, 2872, 957, 25, 10, 81, 504, 2289, 6960, 12380, 10132, 2292, 30, 11, 100, 720, 3948, 15477, 39560, 56890, 35383, 5419, 36, 12, 121 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

..9....63....222.....570.....1215......2289......3948.......6372.......9765

.12...159....804....2670.....6960.....15477.....30744......56124......95940

.16...394...2872...12380....39560....104006....238224.....492312.....939360

.20...957..10132...56890...223320....695135...1837752....4302612....9168780

.25..2292..35383..259445..1253190...4623815..14121282...37478718...89241015

.30..5419.122480.1175355..6995660..30625210.108123624..325487010..866361210

.36.12678.420752.5293671.38870136.202067047.825227424.2819002698.8390905692

LINKS

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

FORMULA

Empirical for column k:

k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)

k=2: a(n) = 6*a(n-1) -9*a(n-2) -8*a(n-3) +24*a(n-4) -16*a(n-6)

k=3: [order 8]

k=4: [order 10]

k=5: [order 12]

k=6: [order 14]

k=7: [order 16]

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 + (7/2)*n^2 + (1/2)*n

n=5: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n

n=6: a(n) = n^6 + 6*n^5 + 8*n^4 + (5/3)*n^3 - n^2 + (1/3)*n

n=7: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n

EXAMPLE

Some solutions for n=6 k=4

..3. .2. .1. .0. .1. .3. .1. .0. .0. .1. .0. .2. .4. .3. .0. .4

..3. .0. .0. .3. .3. .4. .4. .2. .3. .4. .4. .4. .2. .4. .4. .4

..1. .3. .1. .0. .3. .4. .2. .4. .1. .1. .0. .2. .0. .2. .2. .2

..0. .4. .4. .3. .0. .0. .1. .0. .2. .4. .2. .4. .2. .4. .1. .4

..2. .0. .0. .2. .3. .0. .2. .4. .3. .2. .0. .0. .4. .1. .1. .2

..1. .0. .1. .4. .4. .4. .3. .4. .4. .3. .2. .0. .0. .3. .2. .4

CROSSREFS

Column 1 is A002620(n+2).

Column 2 is A267960.

Column 3 is A267928.

Diagonal is A268205.

Row 1 is A000027(n+1).

Row 2 is A000290(n+1).

Row 3 is A007531(n+2).

Sequence in context: A267232 A269606 A269640 * A268944 A269537 A269678

Adjacent sequences:  A269406 A269407 A269408 * A269410 A269411 A269412

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 25 2016

STATUS

approved

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Last modified May 12 13:46 EDT 2021. Contains 343823 sequences. (Running on oeis4.)