A268205 -id:A268205 - cp's OEIS frontend

A269409 T(n,k)=Number of length-n 0..k arrays with no repeated value greater than or equal to the previous repeated value.

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

Offset: 1

R. H. Hardin, Feb 25 2016

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

			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

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

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).

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

A268249 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row greater than, and every column greater than or equal to, the previous repeated value.

Original entry on oeis.org

2, 9, 4, 60, 81, 8, 570, 3600, 729, 15, 6960, 324900, 216000, 6084, 28, 104006, 48441600, 185193000, 12067722, 49284, 51, 1837752, 10817248036, 337153536000, 98956027822, 648144348, 386884, 92, 37478718, 3377332413504, 1125058699232216

Offset: 1

R. H. Hardin, Jan 29 2016

Table starts
...2........9............60...............570.................6960
...4.......81..........3600............324900.............48441600
...8......729........216000.........185193000.........337153536000
..15.....6084......12067722.......98956027822.....2213773305829075
..28....49284.....648144348....50740994294843.13958709698552890082
..51...386884...33600202086.25094770808231271
..92..2965284.1691726672094
.164.22268961
.290

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

R. H. Hardin, Table of n, a(n) for n = 1..48

Column 1 is A029907(n+1).
Column 2 is A268014.
Column 3 is A267977.
Row 1 is A268205.
Row 2 is A268206.

Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
k=2: [order 15]

cp's OEIS Frontend

A269409 T(n,k)=Number of length-n 0..k arrays with no repeated value greater than or equal to the previous repeated value.

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