A267960 -id:A267960 - cp's OEIS frontend

A268026 T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

3, 9, 9, 27, 81, 24, 78, 729, 576, 63, 222, 6084, 13824, 3969, 159, 622, 49284, 295962, 250047, 25281, 394, 1722, 386884, 6042732, 13530274, 4019679, 155236, 957, 4719, 2965284, 117582228, 687233742, 528293442, 61162984, 915849, 2292, 12821

Offset: 1

R. H. Hardin, Jan 24 2016

Table starts
.....3.........9............27..............78...............222
.....9........81...........729............6084.............49284
....24.......576.........13824..........295962...........6042732
....63......3969........250047........13530274.........687233742
...159.....25281.......4019679.......528293442.......64075543999
...394....155236......61162984.....19177213020.....5458407864352
...957....915849.....876467493....642612340592...420621575011611
..2292...5253264...12040481088..20358126145678.30224756956473940
..5419..29365561..159131975059.612589053437088
.12678.160731684.2037756289752

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

R. H. Hardin, Table of n, a(n) for n = 1..84

Column 1 is A267960.
Column 2 is A267961.
Row 1 is A268013.
Row 2 is A268014.

Empirical for column k:
k=1: a(n) = 6*a(n-1) -9*a(n-2) -8*a(n-3) +24*a(n-4) -16*a(n-6)
k=2: [order 15]
k=3: [order 28]
Empirical for row n:
n=1: a(n) = 6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6)
n=2: [order 15]
n=3: [order 86] for n>87

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

Original entry on oeis.org

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

cp's OEIS Frontend

A268026 T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

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