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 13 results. Next

A264359 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

9, 36, 169, 784, 3600, 16641, 76729, 354025, 1633284, 7535025, 34762816, 160376896, 739894401, 3413480625, 15747991081, 72652889764, 335181944601, 1546351938576, 7134048689296, 32912721515521, 151841862142569, 700517916355401
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 3 of A264364.

Examples

			Some solutions for n=4
..6..7..0..1....0..7..2..3....0..1..2..3....6..7..0..1....0..1..2..3
.10..5..2..3....4..1..6..5...10.11..4..7...10..5..2..3...10..5..6..7
..4.15..8..9....8..9.10.11....8..5..6..9....4..9..8.11....4.15..8..9
.18.19.12.11...18.19.12.13...18.19.12.13...18.19.14.15...18.13.12.11
.16.13.14.17...16.17.14.15...16.17.14.15...12.13.16.17...16.17.14.19

Links

Crossrefs

Cf. A264364.

Formula

Empirical: a(n) = 3*a(n-1) +7*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -a(n-6).
Empirical G.f.: -x*(-9-9*x+2*x^2+2*x^3-2*x^4+x^5) / ( (x^3 -x^2 -2*x-1) *(x^3-2*x^2+5*x-1) ). - R. J. Mathar, Dec 09 2015

A264360 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

18, 120, 936, 7168, 54720, 418992, 3204336, 24514000, 187528608, 1434558960, 10974201216, 83950973056, 642212998704, 4912836726000, 37582492431888, 287500651922848, 2199338537486832, 16824622797993408, 128705939150098368
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Examples

			Some solutions for n=4:
..0..1..2..3..4....0..1..2..3..4....7..8..2..1..4....0..1..2..3..4
..5..6..7..8..9....5.13.14..8..7....0..6..5..3..9...12..6..7..8..9
.10.11.12.13.14...10..6.19.11..9...10.11.12.13.14....5.18.10.11.14
.15.16.24.18.19...15.23.12.18.17...22.16.17.18.19...22.16.17.13.19
.20.21.17.23.22...20.16.22.21.24...15.21.20.23.24...15.21.20.23.24

Links

Crossrefs

Column 4 of A264364.

Formula

Empirical: a(n) = 3*a(n-1) + 28*a(n-2) + 57*a(n-3) + 10*a(n-4) - 24*a(n-5) + 8*a(n-6).
Empirical g.f.: 2*x*(9 + 33*x + 36*x^2 - 13*x^3 - 6*x^4 + 4*x^5) / (1 - 3*x - 28*x^2 - 57*x^3 - 10*x^4 + 24*x^5 - 8*x^6). - Colin Barker, Jan 07 2019

A264361 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

36, 400, 5184, 65536, 831744, 10549504, 133818624, 1697440000, 21531453696, 273119121664, 3464422799616, 43945019842816, 557427566889216, 7070778289926400, 89690407502010624, 1137692184365383936
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Examples

			Some solutions for n=4:
..0..9.10.11..2..3....8..1..0..3..2..5....8..9..2..1..4..5....0..9.10..3..2..5
..6..1..8..7..4..5....6.15.16..9..4.11....0..7..6..3.10.11....6..1..8.17..4.11
.12.21.14.13.16.15...12..7.22.23.10.17...20.21.14.23.16.15...12..7.14.13.16.15
.26.27.28.29.20.17...26.13.14.29.20.21...12.13.18.19.22.17...26.27.28.19.20.23
.18.19.24.25.22.23...18.19.24.25.28.27...24.25.26.27.28.29...18.25.24.21.22.29

Links

Crossrefs

Column 5 of A264364.

Formula

Empirical: a(n) = 11*a(n-1) + 22*a(n-2) - 8*a(n-3).
Empirical g.f.: 4*x*(9 + x - 2*x^2) / ((1 + 2*x)*(1 - 13*x + 4*x^2)). - Colin Barker, Jan 07 2019

A264362 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

78, 1440, 33408, 730368, 16066704, 353333680, 7767356736, 170773835200, 3754476071280, 82543032602992, 1814726100469488, 39897129815403584, 877146760653765696, 19284254647180360880, 423968366892038460336
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 6 of A264364.

Examples

			Some solutions for n=3
..9..1..2..3..4..5..6....0..1..2..3.13..5..4....0.10..2.12..4..3..6
..0..8..7.10.11.12.13....7..8..9.10.11.12..6...16..1.18..8..9..5.11
.14.24.25.17.27.19.18...14.24.16.17.27.19.20....7.24.14.15.27.19.13
.21.15.16.22.23.26.20...21.15.23.22.18.26.25...21.22.23.17.25.26.20

Links

Crossrefs

Cf. A264364.

Formula

Empirical: a(n) = 21*a(n-1) +59*a(n-2) -666*a(n-3) -3991*a(n-4) +12120*a(n-5) +20965*a(n-6) -129645*a(n-7) +341857*a(n-8) +5426883*a(n-9) -9160816*a(n-10) -3733596*a(n-11) +126453658*a(n-12) -417161571*a(n-13) +465368456*a(n-14) -225117075*a(n-15) -303829226*a(n-16) +844092492*a(n-17) -326894784*a(n-18) -180879696*a(n-19) +174340672*a(n-20) +47719872*a(n-21) +92096640*a(n-22) -47798016*a(n-23) +5112320*a(n-24) +15599616*a(n-25) +14057472*a(n-26) +6856704*a(n-27) +1646592*a(n-28) +294912*a(n-29) +32768*a(n-30)

A264363 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

169, 5184, 215296, 8139609, 310358689, 11834176225, 450847788304, 17180991840016, 654674355426025, 24946448969913601, 950585713755901609, 36222101462252160016, 1380244690837659186576, 52594277751165110245321
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Column 7 of A264364.

Examples

			Some solutions for n=2
..0..1.12..3.14.15..4..5...10..1..2.13..4..5..6..7....0.11.12..1..2.15..6..7
.18.19..2..9.10.23..6..7....0.19.20..3.22.11.12.15...18..9..8..3..4..5.14.13
..8.17.16.11.20.13.22.21....8..9.16.17.18.21.14.23...16.17.10.19.20.21.22.23

Links

Crossrefs

Cf. A264364.

A264365 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

1, 3, 9, 18, 36, 78, 169, 364, 784, 1680, 3600, 7740, 16641, 35733, 76729, 164815, 354025, 760410, 1633284, 3508110, 7535025, 16184520, 34762816, 74666944, 160376896, 344473464, 739894401, 1589218425, 3413480625, 7331811675
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Examples

			Some solutions for n=4:
..7..8..0..3..4....0..1..2..3..4....0..8..9..3..4....0..8..2..3..4
..5..1..2..6..9....5..6..7..8..9....5..1..2..6..7....5..1..7..6..9

Links

Crossrefs

Row 1 of A264364.

Formula

Empirical: a(n) = a(n-1) + 3*a(n-3) + 3*a(n-4) + 3*a(n-5) + 3*a(n-6) - 2*a(n-8) - a(n-9).
Empirical g.f.: x*(1 + 2*x + 6*x^2 + 6*x^3 + 6*x^4 + 3*x^5 - 2*x^6 - 3*x^7 - x^8) / ((1 + x^2 - x^3)*(1 + x^2 + x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jan 07 2019

A264366 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

1, 6, 36, 120, 400, 1440, 5184, 18432, 65536, 233472, 831744, 2962176, 10549504, 37572864, 133818624, 476601600, 1697440000, 6045523200, 21531453696, 76685407488, 273119121664, 972728179968, 3464422799616, 12338724758784
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Examples

			Some solutions for n=4:
..0..8..2..1..4....0..8..9..3..4....0..8..2..3..4....7..1..0..3..2
..5..6.14..3..7...12..1..2..6..7....5..1..7..6..9....5..6.14..8..4
.10.11.12.13..9....5.11.10.13.14...10.11.12.13.14...10.11.12.13..9

Links

Crossrefs

Row 2 of A264364.

Formula

Empirical: a(n) = 3*a(n-1) + 6*a(n-3) + 4*a(n-4).
Empirical g.f.: x*(1 + 3*x + 18*x^2 + 6*x^3) / ((1 + 2*x^2)*(1 - 3*x - 2*x^2)). - Colin Barker, Jan 07 2019

A264367 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

1, 13, 169, 936, 5184, 33408, 215296, 1323792, 8139609, 50261301, 310358689, 1916465345, 11834176225, 73043905820, 450847788304, 2783165854192, 17180991840016, 106056375378580, 654674355426025, 4041262228505645
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 3 of A264364.

Examples

			Some solutions for n=4
..7..1..0..3..4....7..1..0..3..4....0..8..9..3..2....7..1..0..3..4
..5..6..2..8..9....5..6..2..8..9....5..1.14..6..4...12..6..2..8..9
.10.18.19.13.12...10.18.12.13.14...10.18..7.13.12....5.18.19.11.14
.15.11.17.16.14...15.11.17.16.19...15.11.17.16.19...10.16.15.13.17

Links

Crossrefs

Cf. A264364.

A264368 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

1, 28, 784, 7168, 65536, 730368, 8139609, 86397399, 917060089, 9745523645, 103564894225, 1098865637220, 11659411209744, 123652174760256, 1311374995519744, 13905429141268656, 147449021266573569
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 4 of A264364.

Examples

			Some solutions for n=4
..0..8..9..3..4....7..8..9..1..2....7..1..9..3..2....0..1..9..3..2
..5..1..2..6..7....0.13.14..3..4....0.13..5..6..4....5..6..7..8..4
.17.11.10.13.14....5..6.10.11.12...10.11.12..8.14...10.11.12.13.14
.22.23.12.16.19...15.23.17.16.19...22.23.17.16.19...22.16.15.18.19
.15.21.20.18.24...20.21.22.18.24...15.21.20.18.24...20.21.17.23.24

Links

Crossrefs

Cf. A264364.

A264369 Number of (5+1) X (n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

Original entry on oeis.org

1, 60, 3600, 54720, 831744, 16066704, 310358689, 5669414855, 103564894225, 1897896238940, 34780223170576, 635711773067072, 11619518840752384, 212144954220192048, 3873265512788926881, 70687878202585153191
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2015

Keywords

Comments

Row 5 of A264364.

Examples

			Some solutions for n=4
..0..8..9..1..2....0..1..2..3..4....7..1..0..3..2....0..8..2..3..4
..5..6.14..3..4...12..6..5..8..9...12..6.14..8..4....5..1..7..6..9
.10.18..7.13.12...10.18..7.11.14....5.11.10.13..9...17.18.10.13.14
.15.11.17.16.19...15.16.17.13.19...15.23.24.16.17...22.11.12.16.19
.27.28.20.21.24...27.28.29.21.22...27.28.22.18.19...15.28.20.23.24
.25.26.22.23.29...20.26.25.23.24...20.21.25.26.29...25.21.27.26.29

Links

Crossrefs

Cf. A264364.
Showing 1-10 of 13 results. Next

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

Content is available under The OEIS End-User License Agreement.