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 1-9 of 9 results.

A264014 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, 105, 1573, 20570, 269225, 3524125, 46131250, 603865625, 7904703125, 103473906250, 1354491015625, 17730517578125, 232095488281250, 3038169384765625, 39770153564453125, 520598068847656250
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Examples

			Some solutions for n=4:
.12.13..9..3..4....7..1..9..3..4....7.13.14..3..4....7.13..9..3..4
..5..6.19..8..2....5.18..0..8..2...17.18.19..8..9...12.18..0..8..2
.10.18..0..1.14...10.11.24.13.14...10.11..0..1..2...17.23..5..1.14
.22.16.24.11..7...22.23.17..6.19...15.23..5..6.12...22.16.10..6.19
.20.21.15.23.17...20.21.15.16.12...20.21.22.16.24...20.21.15.11.24

Links

Crossrefs

Column 4 of A264017.

Formula

Empirical: a(n) = 15*a(n-1) - 25*a(n-2) for n>4.
Empirical g.f.: x*(1 - 2*x)*(8 + x + 200*x^2) / (1 - 15*x + 25*x^2). - Colin Barker, Jan 03 2019

A264015 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, 1869, 146410, 7320500, 398967250, 21860843125, 1201888840625, 66099082156250, 3635200164062500, 199922408907031250, 10994987257267578125, 604683325796494140625, 33255329542371191406250, 1828919197622934570312500
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Examples

			Some solutions for n=3:
..9..1.11.12.13..5..6....0..1..2..3.20..5..6....9.10.18.19..4..5..6
..7.24..0.19.27..3..4...16..8.25.19.11.12.13....7.24..0.26.27.12.13
.23.15.16.26..2.10.20...23.15..7.26.18.10..4...23.15.25..1..2..3.20
.21.22.14..8.25.17.18...21.22.14.24..9.17.27...21.22.14..8.16.17.11

Links

Crossrefs

Column 6 of A264017.

Formula

Empirical: a(n) = 60*a(n-1) - 300*a(n-2) + 1500*a(n-3) - 7500*a(n-4) + 3125*a(n-5) for n>7.
Empirical g.f.: x*(32 - 51*x + 43870*x^2 - 951400*x^3 + 1096750*x^4 - 86739375*x^5 + 39912500*x^6) / ((1 - 5*x)*(1 - 55*x + 25*x^2 - 1375*x^3 + 625*x^4)). - Colin Barker, Jan 03 2019

A264016 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, 7921, 1464100, 146410000, 17394972100, 2089022169025, 252579343635025, 30557658560100100, 3696969485250250000, 447272452462938576100, 54112631066129736180025, 6546741114347411138472025
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Comments

Column 7 of A264017.

Examples

			Some solutions for n=2
..0.11.20..3.14.15..6..7....0..1.12..3.22..5..6..7...10..1..2..3.14.15..6..7
.18..9.10..1.22.13..4..5....8..9.20.11..2.23.14.15...18..9..0.21.12.23..4..5
.16.17..8.19..2.21.12.23...16.17.18.19.10.21..4.13...16.17..8.19.20.11.22.13

Links

Crossrefs

Cf. A264017.

Formula

Empirical: a(n) = 130*a(n-1) -1191*a(n-2) +13340*a(n-3) -146501*a(n-4) -159459*a(n-5) -1321*a(n-6) +1321*a(n-7) +159459*a(n-8) +146501*a(n-9) -13340*a(n-10) +1191*a(n-11) -130*a(n-12) +a(n-13) for n>15.

A264018 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, 5, 25, 105, 441, 1869, 7921, 33553, 142129, 602069, 2550409, 10803705, 45765225, 193864605, 821223649, 3478759201, 14736260449, 62423800997, 264431464441, 1120149658761, 4745030099481, 20100270056685, 85146110326225
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Examples

			Some solutions for n=4:
..7..1..2..3..4....0.13..9..3..4....0..8..9..3..4....7..1..9..3..4
.12..6..0..8..9...12..6..7..8..2...12..6.14..1..2...12.13..0..8..2
.10.11..5.13.14...10.11..5..1.14...10.11..5.13..7...10.11..5..6.14

Links

Crossrefs

Row 2 of A264017.

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-3) + a(n-4).
Empirical g.f.: x*(1 + x + 5*x^2 + x^3) / ((1 + x^2)*(1 - 4*x - x^2)). - Colin Barker, Jan 03 2019
Empirical: 5*a(n) = 2*A228826(n) + A048876(n). - R. J. Mathar, Sep 09 2020

A264019 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, 34, 1156, 20570, 366025, 7320500, 146410000, 2898918000, 57398576400, 1136955639600, 22520909184400, 446088564737200, 8836011280003600, 175021631355863600, 3466787272192723600, 68669304273355566000
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Examples

			Some solutions for n=4:
..7..8..2..3..4....7..8..9..3..4....7..8..2..3..4....0..1..2..3..4
..5.13.19..1..9...17.13.19..1..2...17.13..0..1..9....5.13.14..8..9
.10.11..0..6.14...10.23..0..6.14...22.23.12..6.14...10.11.24..6..7
.15.23.24.18.12...22.16..5.18.12...15.16..5.18.19...15.16.17.18.19
.20.21.22.16.17...20.21.15.11.24...20.21.10.11.24...20.21.22.23.12

Links

Crossrefs

Row 4 of A264017.

Formula

Empirical: a(n) = 19*a(n-1) + 304*a(n-3) + 256*a(n-4) for n>8.
Empirical g.f.: x*(1 + 15*x + 510*x^2 - 1698*x^3 - 35397*x^4 + 5897*x^5 + 771284*x^6 + 590480*x^7) / ((1 + 16*x^2)*(1 - 19*x - 16*x^2)). - Colin Barker, Jan 03 2019

A264020 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, 89, 7921, 269225, 9150625, 398967250, 17394972100, 744568640640, 31870270181376, 1369690710968448, 58865288340403204, 2529832159410757762, 108723679696921023361, 4672588420041689987741, 200812579228092423992521
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Comments

Row 5 of A264017.

Examples

			Some solutions for n=3
..0..1..2..3...10.11..2..3....0..1..2..3....6..1..2..3....6..1..2..3
..4.15..6..7....4.15..6..7...10..5..6..7....4.11..0..7...10..5..0..7
.14..9.10.11....8.19..0..1...18.19..4.11...18.15.10..5...18.15..4.11
.18.19..8..5...12.23.14..5...12.13.14.15...12.13.14..9...12.13.14..9
.22.23.12.13...22.17.18..9...16.23..8..9...22.23..8.19...22.23..8.19
.20.21.16.17...20.21.16.13...20.21.22.17...20.21.16.17...20.21.16.17

Links

Crossrefs

Cf. A264017.

Formula

Empirical: a(n) = 43*a(n-1) -a(n-2) +1848*a(n-4) -79464*a(n-5) +1848*a(n-6) -1848*a(n-8) +79464*a(n-9) -1848*a(n-10) +a(n-12) -43*a(n-13) +a(n-14) for n>18

A264021 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, 233, 54289, 3524125, 228765625, 21860843125, 2089022169025, 188902868291280, 17081816640235776, 1556476909654928976, 141824515583579002801, 12912728820640619613016, 1175668148128746582139456
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Comments

Row 6 of A264017.

Examples

			Some solutions for n=3
..6.11..2..3....6..7..2..3....6..7..2..3....0.11..2..3....0..1..2..3
..4.15..0..7...14.11..0..1...10.11..0..1....4..5..6..7....4.11..6..7
..8..9.10..1...18.15.10..5...18.15..4..5...18.15.10..1....8..9.10..5
.18.13.14..5...12.23..4..9...22.13.14..9...12.23.14..9...22.23.14.15
.16.17.12.19...26.17..8.19...16.27..8.19...26.17..8.19...26.17.18.19
.26.21.22.23...20.27.22.13...26.21.12.23...20.27.22.13...20.27.12.13
.24.25.20.27...24.25.16.21...24.25.20.17...24.25.16.21...24.25.16.21

Links

Crossrefs

Cf. A264017.

Formula

Empirical: a(n) = 87*a(n-1) +32068*a(n-3) +180766*a(n-4) -3715198*a(n-5) -16639004*a(n-6) +149707392*a(n-7) +542256817*a(n-8) +224301365*a(n-9) +4280490864*a(n-10) -2613943512*a(n-11) +12541107972*a(n-12) -12056948868*a(n-13) +9621158616*a(n-14) -5946708960*a(n-15) -2779571151*a(n-16) +6286349025*a(n-17) -2468635920*a(n-18) -364811148*a(n-19) +148489470*a(n-20) -3874014*a(n-21) +2657124*a(n-22) +16767*a(n-24) +243*a(n-25) for n>31

A264022 Number of (7+1)X(n+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

1, 610, 372100, 46131250, 5719140625, 1201888840625, 252579343635025, 48585262182665120, 9345687843615794176, 1837459507629935674144, 361263664983848912725561, 70936527322260095931846664
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Comments

Row 7 of A264017.

Examples

			Some solutions for n=2
..5..1..2....0..1..2....0..1..2....8..1..2....5..1..2....0..1..2....5..1..2
..8..4..0....3..4..5....8..4..5...11..4..5...11..4..0....3..4..5...11..4..0
.14..7..3...14..7..8...11..7..3...14..7..0....6..7..8....6..7..8...14..7..8
..9.10.11...17.10.11....9.10..6....9.10..3...14.10..3....9.10.11....9.10..3
.12.13..6...20.13..6...20.13.14...17.13..6...17.13..9...17.13.14...17.13..6
.20.16.17...23.16..9...15.16.17...20.16.12...20.16.12...15.16.12...23.16.12
.18.19.15...18.19.12...23.19.12...18.19.15...18.19.15...23.19.20...18.19.20
.21.22.23...21.22.15...21.22.18...21.22.23...21.22.23...21.22.18...21.22.15

Links

Crossrefs

Cf. A264017.

A264013 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, 5, 169, 20570, 9150625, 21860843125, 252579343635025, 12379056073433237760
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2015

Keywords

Comments

Diagonal of A264017.

Examples

			Some solutions for n=4
..7..1.14..3..4....0..8.14..3..4....0..1..2..3..4...12..8.14..3..4
.12.13..0..8..9...17..6..7..1..9...12..6.19..8..9....5.18..0..1..9
.10.11.24..6..2...22.23.12.13..2...10.18.24.13.14...22.11.19.13..2
.15.23..5.18.19...15.16..5.18.19...15.23..5.11..7...15.23.17..6..7
.20.21.22.16.17...20.21.10.11.24...20.21.22.16.17...20.21.10.16.24

Crossrefs

Cf. A264017.
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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