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 1-10 of 11 results. Next

A264054 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

2, 8, 18, 45, 125, 320, 832, 2197, 5733, 14994, 39304, 102850, 269225, 704969, 1845504, 4831488, 12649337, 33116057, 86698690, 226981000, 594243090, 1555747893, 4073003173, 10663258432, 27916771136, 73087061741, 191344405725
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Column 2 of A264059.

Examples

			Some solutions for n=4:
..5..1..6....5..1..6....0..1..6....0..1..6....5..1..2....0..1..2....5..1..6
..3..4..0....3..4..0....8..4..5....3..4..5....8..4..0....8..4..9....3..4..0
..2..7..8....2..7.12....2..7..3....2..7.12...11..7..3...11..7..3....2..7.12
.14.10.11...14.10.11....9.10.11....9.10.11....9.10..6....5.10..6....9.10.11
.12.13..9....8.13..9...12.13.14....8.13.14...12.13.14...12.13.14....8.13.14

Links

Crossrefs

Cf. A264059.

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) - 9*a(n-4) + 3*a(n-5) - a(n-6) + 3*a(n-7) - a(n-8).
Empirical g.f.: x*(2 + 2*x - 4*x^2 - 7*x^3 + 2*x^4 + 2*x^5 + 2*x^6 - x^7) / ((1 - 3*x + x^2)*(1 - 3*x^3 + x^6)). - Colin Barker, Mar 20 2018

A264055 Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

4, 64, 324, 2025, 15625, 102400, 692224, 4826809, 32867289, 224820036, 1544804416, 10578122500, 72482100625, 496981290961, 3405885014016, 23343276294144, 160005726539569, 1096673231227249, 7516662847716100, 51520374361000000
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Column 3 of A264059.

Examples

			Some solutions for n=4
..0..1..2..3....6..1..2..9....0..7..8..9....0..1..2..9....0..7..2..9
.10..5..6.13....4..5..0..7....4..5..6..1....4..5..6..7....4..5..6..1
..8..9..4.17....8..3.16.17....2..3.10.17....8..3.10.17...14..3.16.17
.18..7.14.15...18.13.14.15...12.19.14.15...18.19.14.15...12.19..8.15
.16.11.12.19...10.11.12.19...16.11.18.13...16.11.12.13...10.11.18.13

Links

Crossrefs

Cf. A264059.

Formula

Empirical: a(n) = 7*a(n-1) -a(n-2) +55*a(n-3) -385*a(n-4) +55*a(n-5) -385*a(n-6) +2695*a(n-7) -385*a(n-8) +385*a(n-9) -2695*a(n-10) +385*a(n-11) -55*a(n-12) +385*a(n-13) -55*a(n-14) +a(n-15) -7*a(n-16) +a(n-17).

A264056 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

8, 216, 2592, 32400, 450000, 5760000, 74880000, 988650000, 12899250000, 168682500000, 2210850000000, 28926562500000, 378597656250000, 4956813281250000, 64881000000000000, 849285000000000000
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Column 4 of A264059.

Examples

			Some solutions for n=4
..0..8.10.11..4....0..8..2.11.12....0..1.10..3.12....0..1..2..3..4
..5..6..7..1..2....5..6..7..1..9....5.13.15.16..9....5..6..7.16..9
.17..3.19.21.14...10..3..4.21.14....2.18..4..6..7...10.11.20.21.14
.15.16..9.18.12...22.16.24.18.19...22..8.24.11.19...22..8.17.18.19
.20.13.22.23.24...20.13.15.23.17...20.21.14.23.17...12.13.15.23.24

Links

Crossrefs

Cf. A264059.

Formula

Empirical: a(n) = 15*a(n-1) -25*a(n-2) +375*a(n-3) -5625*a(n-4) +9375*a(n-5) -15625*a(n-6) +234375*a(n-7) -390625*a(n-8) for n > 10.

A264057 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

32, 3375, 207360, 11151360, 608212800, 34260048000, 1869178500000, 102920833800000, 5656555271250000, 310843030421250000, 17102133249581250000, 940367566368000000000, 51715504235250000000000
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Column 6 of A264059.

Examples

			Some solutions for n=2
..9.10..2.15..4..5..6....0..1.14.15.16..5..6....0.10.14..3.16..5.18
.16.17..0..1.11.12.13....7.17..9.19.20.12.13....7.17..9..1.11.12.13
.14..3..7..8.18.19.20....2..3..4..8.18.10.11....2.15..4..8..6.19.20

Links

Crossrefs

Cf. A264059.

A264058 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

64, 15625, 2073600, 239878144, 28543426704, 3622687928896, 431336822822500, 52309619901665296, 6320319513423439225, 763444065670843677649, 92439059495958921766969, 11179187008813825703018496
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Column 7 of A264059.

Examples

			Some solutions for n=2
.10.11.16.17..4..5..6..7...10..1..2.13..4..5.20..7...10.11..2.17.18.15.20.21
.18.19..0..1.22.13.14.15...18.19..0.21.22..3.14.15....8..9..0..1.22.13.14..5
..2..3..8..9.20.21.12.23...16.17..8..9..6.11.12.23...16..3..4.19..6..7.12.23

Links

Crossrefs

Cf. A264059.

A264060 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

1, 8, 64, 216, 729, 3375, 15625, 64000, 262144, 1124864, 4826809, 20346417, 85766121, 363994344, 1544804416, 6539203000, 27680640625, 117289217375, 496981290961, 2105026154496, 8916100448256, 37770717892608, 160005726539569
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Row 2 of A264059.

Examples

			Some solutions for n=4
..0..1..2.11..4....7..1..2..3..4....7..8.10.11.12....0..1.10..3..4
..5..6.14..8..9...12..6..0..8..9....5..6..0..1..9....5..6.14..8..9
.10..3.12.13..7...10.11..5.13.14....2..3..4.13.14....2.11.12.13..7

Links

Crossrefs

Cf. A264059.

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +20*a(n-3) +20*a(n-4) -60*a(n-5) -60*a(n-7) -20*a(n-8) +20*a(n-9) +4*a(n-10) +4*a(n-11) +a(n-12).

A264061 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

1, 45, 2025, 32400, 518400, 11151360, 239878144, 4614184960, 88756326400, 1773696512000, 35445352960000, 699751279718400, 13814275005812736, 273958624952463360, 5433026934403993600, 107577300516952780800
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Row 4 of A264059.

Examples

			Some solutions for n=4
..0..1..2..3..4....0..1.10..3..4....7..8..9.11.12....0..1..9..3..4
.12..6.14..8.17....5.13.14.16..2....5..6..0..1..2....5..6.15.16..2
.10.18..5.13..7...17.11.20..6.22...10..3..4.13.14...10.11.19.13.14
.15.23..9.11.19....7..8..9.18.19...22.16.17.18.19....7..8.17.18.12
.20.21.22.16.24...12.21.15.23.24...20.21.15.23.24...20.21.22.23.24

Links

Crossrefs

Cf. A264059.

Formula

Empirical: a(n) = 19*a(n-1) +16*a(n-2) -2366480*a(n-6) +44963120*a(n-7) +37863680*a(n-8) +238086819840*a(n-12) -4523649576960*a(n-13) -3809389117440*a(n-14) +975203614064640*a(n-18) -18528868667228160*a(n-19) -15603257825034240*a(n-20) -162623267306209280*a(n-24) +3089842078817976320*a(n-25) +2601972276899348480*a(n-26) -1152921504606846976*a(n-30) +21905508587530092544*a(n-31) +18446744073709551616*a(n-32)

A264053 Number of (n+1)X(n+1) arrays of permutations of 0..(n+1)^2-1 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

1, 8, 324, 32400, 12960000, 34260048000, 431336822822500
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Diagonal of A264059.

Examples

			Some solutions for n=4
..0..1..2.11.12....0..8..9..3..4....0..8.10..3.12....0..1..2.11..4
..5..6.14..8..9....5..6.15..1..2....5..6.14..1..2....5..6.15.16..9
.17..3..4.13.22...17.11.19.13.14...17.11..4.13..7...10..3.19.21..7
..7.23.10.18.19....7.23.10.18.12...22.16..9.18.19...22..8.24.18.12
.20.21.15.16.24...20.21.22.16.24...20.21.15.23.24...20.13.14.23.17

Crossrefs

Cf. A264059.

A264062 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

1, 125, 15625, 450000, 12960000, 608212800, 28543426704, 1182858335568, 49018425731856, 2119255344115812, 91623571065536449, 3925600962291584977, 168191904505904029921, 7232349156077380791312
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Row 5 of A264059.

Examples

			Some solutions for n=3
..6..1..2..3....6..1..2..9....6..7..2..3....6..7..2..3....6..1..2..3
..4..5..0..7...10..5..0..7....4.11..0..1...10..5..0..1...10..5..0..7
.14..9.10.11...14..3..4.11...14..9.10..5....8..9..4.17....8.15..4.17
.12.19..8.21...18.19..8.15...18.19..8.21...12.19.14.15...12.19.20..9
.16.17.18.13...22.17.12.13...16.23.12.13...16.11.18.13...16.11.18.13
.20.15.22.23...20.21.16.23...20.15.22.17...20.21.22.23...14.21.22.23

Crossrefs

Cf. A264059.

A264063 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.

Original entry on oeis.org

1, 320, 102400, 5760000, 324000000, 34260048000, 3622687928896, 311933405047264, 26859186077900176
Offset: 1

Views

Author

R. H. Hardin, Nov 02 2015

Keywords

Comments

Row 6 of A264059.

Examples

			Some solutions for n=3
..0..7..2..9....0..1..8..9....0..1..2..9....6..1..8..9....0..7..8..3
..4..5.12..1....4..5..6.13...10.11.12..7...10..5..0.13....4.11.12..1
.14..3.10.11....2..3.10.17....8..3..4..5....2..3..4.11....2..9.10..5
..6.19..8.15...12..7.14.15....6.19.20.21...18..7.14.15....6.19.14.15
.22.17.24.13...16.11.24.25...22.23.18.13...22.23.12.19...16.17.18.13
.26.21.16.23...20.21.22.23...14.15.16.17...26.21.16.17...26.27.22.23
.18.25.20.27...18.19.26.27...24.25.26.27...24.25.20.27...24.25.20.21

Crossrefs

Cf. A264059.
Showing 1-10 of 11 results. Next

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