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.

A281605 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 2, 2, 4, 9, 5, 11, 29, 50, 14, 30, 110, 209, 285, 41, 82, 442, 1283, 1623, 1617, 122, 224, 1708, 8180, 16198, 12413, 9188, 365, 612, 6596, 49572, 167545, 203276, 95623, 52193, 1094, 1672, 25624, 302304, 1626073, 3401430, 2563481, 736757, 296511, 3281, 4568
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2017

Keywords

Comments

Table starts
....1.......2.........4..........11.............30.............82
....2.......9........29.........110............442...........1708
....5......50.......209........1283...........8180..........49572
...14.....285......1623.......16198.........167545........1626073
...41....1617.....12413......203276........3401430.......52899445
..122....9188.....95623.....2563481.......69506779.....1732267694
..365...52193....736757....32354824.....1421127262....56764280423
.1094..296511...5678559...408458506....29066686772..1860912910152
.3281.1684466..43771933..5156857179...594539026170.61012156448915
.9842.9569425.337417047.65107404580.12161158312943

Examples

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

Links

Crossrefs

Column 1 is A007051(n-1).
Column 2 is A231413(n-1).
Row 1 is A021006(n-3).
Row 2 is A280853.

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: a(n) = 7*a(n-1) +10*a(n-2) -26*a(n-3) -64*a(n-4) -40*a(n-5) for n>6
k=4: [order 16] for n>18
k=5: [order 40] for n>42
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
n=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
n=3: [order 13] for n>15
n=4: [order 55] for n>58

A280362 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.

Original entry on oeis.org

1, 2, 2, 4, 9, 4, 11, 50, 50, 11, 30, 285, 571, 285, 30, 82, 1617, 6727, 6727, 1617, 82, 224, 9188, 78800, 164326, 78800, 9188, 224, 612, 52193, 924579, 3992071, 3992071, 924579, 52193, 612, 1672, 296511, 10844773, 97147710, 201054068, 97147710
Offset: 1

Views

Author

R. H. Hardin, Jan 01 2017

Keywords

Comments

Table starts
....1.......2...........4.............11...............30................82
....2.......9..........50............285.............1617..............9188
....4......50.........571...........6727............78800............924579
...11.....285........6727.........164326..........3992071..........97147710
...30....1617.......78800........3992071........201054068.......10144351660
...82....9188......924579.......97147710......10144351660.....1061399606602
..224...52193....10844773.....2363431872.....511688896140...111020011111453
..612..296511...127214104....57503068637...25812250379197.11613529410292966
.1672.1684466..1492251709..1399048151083.1302084964081326
.4568.9569425.17504551617.34038954765446

Examples

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

Links

Crossrefs

Column 1 is A021006(n-3).
Column 2 is A231413(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: [order 12]
k=4: [order 44]

A274065 T(n,k)=Number of nXk 0..2 arrays with no three equal values forming an isosceles right triangle, and new values introduced in 0..2 order.

Original entry on oeis.org

1, 2, 2, 5, 9, 5, 14, 50, 50, 14, 41, 285, 264, 285, 41, 122, 1617, 435, 435, 1617, 122, 365, 9188, 546, 8, 546, 9188, 365, 1094, 52193, 1209, 1, 1, 1209, 52193, 1094, 3281, 296511, 3272, 0, 0, 0, 3272, 296511, 3281, 9842, 1684466, 8412, 0, 0, 0, 0, 8412, 1684466, 9842
Offset: 1

Views

Author

R. H. Hardin, Jun 09 2016

Keywords

Comments

Table starts
.....1.......2.....5..14...41..122...365...1094....3281....9842.29525
.....2.......9....50.285.1617.9188.52193.296511.1684466.9569425
.....5......50...264.435..546.1209..3272...8412...20634
....14.....285...435...8....1....0.....0......0
....41....1617...546...1....0....0.....0
...122....9188..1209...0....0....0
...365...52193..3272...0....0
..1094..296511..8412...0
..3281.1684466.20634
..9842.9569425
.29525

Examples

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

Links

Crossrefs

Column 1 is A007051(n-1).
Column 2 is A231413(n-1).

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: [order 40] for n>49
Showing 1-3 of 3 results.

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