cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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.

Original entry on oeis.org

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

Views

Author

R. H. Hardin, Jan 24 2016

Keywords

Comments

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

Examples

			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

Links

Crossrefs

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

Formula

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

A268204 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column greater than the previous repeated value.

Original entry on oeis.org

2, 9, 4, 60, 81, 6, 570, 3600, 576, 9, 6960, 324900, 178068, 3969, 12, 104006, 48441600, 157322070, 8459154, 25281, 16, 1837752, 10817248036, 292870561470, 73055876226, 376812420, 155236, 20, 37478718, 3377332413504, 994136348047368
Offset: 1

Views

Author

R. H. Hardin, Jan 28 2016

Keywords

Comments

Table starts
..2......9..........60............570.............6960...............104006
..4.....81........3600.........324900.........48441600..........10817248036
..6....576......178068......157322070.....292870561470......994136348047368
..9...3969.....8459154....73055876226.1699631089239529.87855957137937824257
.12..25281...376812420.32082001964881
.16.155236.16109362560
.20.915849
.25

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2).
Column 2 is A267961.
Column 3 is A267930.

A268246 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row greater than or equal to, and every column greater than, the previous repeated value.

Original entry on oeis.org

2, 9, 4, 64, 81, 6, 615, 4096, 576, 9, 7536, 378225, 216000, 3969, 12, 112476, 56791296, 197555340, 10941048, 25281, 16, 1981512, 12650850576, 371713931400, 98956027822, 519718464, 155236, 20, 40265487, 3926389806144, 1257212773492866
Offset: 1

Views

Author

R. H. Hardin, Jan 29 2016

Keywords

Comments

Table starts
..2......9..........64............615.............7536................112476
..4.....81........4096.........378225.........56791296...........12650850576
..6....576......216000......197555340.....371713931400......1257212773492866
..9...3969....10941048....98956027822.2335306173137957.120138605995104637373
.12..25281...519718464.46876747497685
.16.155236.23689358848
.20.915849
.25

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2).
Column 2 is A267961.
Column 3 is A267971.
Row 1 is A268104.
Row 2 is A268105.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
k=2: [order 15]
k=3: [order 40]
Showing 1-3 of 3 results.

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