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

A264484 Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

1, 3, 4, 12, 25, 52, 121, 261, 576, 1280, 2809, 6204, 13689, 30167, 66564, 146804, 323761, 714136, 1575025, 3473817, 7661824, 16898560, 37271025, 82203912, 181306225, 399883707, 881971204, 1945248444, 4290381001, 9462732780
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Examples

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

Links

Crossrefs

Column 1 of A264490.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3) - 2*a(n-4) + 4*a(n-5) + a(n-6) - a(n-9).
Empirical g.f.: x*(1 + x - 2*x^2 + 3*x^3 - x^7) / ((1 - 2*x - x^3)*(1 + 2*x^4 - x^6)). - Colin Barker, Jan 08 2019

A264485 Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

1, 1, 12, 16, 214, 324, 2960, 6442, 42656, 113575, 636361, 1918550, 9612512, 31689325, 147107038, 515046002, 2273096344, 8287463026, 35352586169, 132498950637, 552353463562, 2109344649645, 8657596384451, 33484770583688
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 2 of A264490.

Examples

			Some solutions for n=4
..8..4..5....3..4..5....8..4..5....3..2..5....8..4..5....8..4..5....3..4..5
..0..1..2....6..1..2....0..7..2....6..7..8....6..1..2....0..7..2....0..1..2
..9.10.11...14..0.11....9.10..1...14..0..1....9..0.11....3.10..1...14.10.11
.12..3.14...12.13..8...12..3.14...12.13..4...12..3.14...12.13.14...12.13..8
.13..6..7....9.10..7...13..6.11....9.10.11...13.10..7....9..6.11....9..6..7

Links

Crossrefs

Cf. A264490.

Formula

Empirical: a(n) = 20*a(n-2) +8*a(n-3) -102*a(n-4) -38*a(n-5) +337*a(n-6) +39*a(n-7) -2538*a(n-8) -1048*a(n-9) +9220*a(n-10) +3898*a(n-11) -10078*a(n-12) +719*a(n-13) +55039*a(n-14) +28538*a(n-15) -139480*a(n-16) -52428*a(n-17) -19106*a(n-18) -17134*a(n-19) -99749*a(n-20) -71330*a(n-21) +298006*a(n-22) +77280*a(n-23) +114868*a(n-24) +14464*a(n-25) +78816*a(n-26) +80368*a(n-27) -280704*a(n-28) -11136*a(n-29) -107712*a(n-30) -5568*a(n-31) -33408*a(n-32) -31104*a(n-33) +93312*a(n-34) -13824*a(n-35) +41472*a(n-36)

A264486 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

1, 10, 36, 212, 2144, 9714, 92052, 581575, 4510937, 31398740, 236553733, 1681262954, 12489549989, 90270132471, 663622115288, 4832089305548, 35389917941640, 258336002558736, 1889497035402309, 13806771114617572
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 3 of A264490.

Examples

			Some solutions for n=4
..4..5..6..7....4..5..6..7....4..5..3..7....4..5..6..7....4..5..3..7
..8..1..2..3....0..1..2.11....0..9..2.11....0..1.10..3....0..1.10.11
.12..0.14.15....9.13..3.15...12.13..1.15...12.13.14..2...12.13.14..2
.16.17.18.11...16.17.18.19...16..6.18.19...16..9.18.19...16.17.18..6
..9.13.19.10...12..8.14.10...17..8.14.10...17..8.11.15....9..8.19.15

Links

Crossrefs

Cf. A264490.

A264487 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

1, 8, 108, 788, 21466, 142352, 2870927, 30309632, 463508815, 5517128232, 80746395988, 996650042932, 14098841570856, 180039273539208, 2481030453759277, 32286677930222166, 438951446059251344
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 4 of A264490.

Examples

			Some solutions for n=4
.12..6..7..4..9....5..6..7..4..9....5..6..7..8..9....5..6..7..8..9
..0..1..2..3.14....0.18.12.13.14...10..1.12.13..4...10.11..2..3..4
..5.16.17.18.19...15.16..1..2..3...11..0.24..2..3...22..0..1.18.19
.20.21.22.23..8...20.11.22.23..8...20.21.22.23.14...20.21.12.23.14
.15.10.11.24.13...21.10.17.24.19...15.16.17.18.19...15.16.17.24.13

Links

Crossrefs

Cf. A264490.

A264488 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

1, 35, 324, 4772, 217049, 2517024, 89130069, 1749889912, 47485981944, 1036062520569, 27578007781836, 620722292448311, 15966382007038680, 373437492628645406, 9348490299717806516, 222809815180956245674
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 5 of A264490.

Examples

			Some solutions for n=4
..6..7..3..9..5.11....6..7..8.17.10.11....6..7..8..9.10.11....6..7..8..9.10.11
.12..1..2.15..4.17...12.13..9..3..4..5....0..1.14..3.16..5...12..1..2..3..4..5
.18..0..8.21.10.23...26..0..1..2.22.23...18.19.20..2.22..4...18..0.20.21.22.23
.24.13.26.27.28.29...24.25.21.27.28.29...24.25.26.27.28.29...24.13.26.15.28.29
.25.19.20.14.22.16...18.19.20.14.15.16...13.12.15.21.17.23...25.19.27.14.17.16

Links

Crossrefs

Cf. A264490.

A264491 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

3, 1, 10, 8, 35, 42, 130, 194, 501, 849, 1979, 3613, 7942, 15145, 32182, 62953, 131165, 260426, 536438, 1074379, 2198378, 4425274, 9019904, 18210519, 37034259, 74898261, 152118445, 307953916, 624975597, 1265962640, 2568054807, 5203674585
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Examples

			Some solutions for n=4:
.12..6..7..4..9....5..6.14..8..9...12..6..7..8..9....5..6.14..8..9
.10.11..2.13.14...10.11.12.13..4...10.11..2.13..4...10..7.12.13..4
..5..0..1..8..3....1..0..7..2..3....5..0..1.14..3...11..0..1..2..3

Links

Crossrefs

Row 2 of A264490.

Formula

Empirical: a(n) = 3*a(n-2) + 2*a(n-3) + a(n-4) - a(n-5).
Empirical g.f.: x*(3 + x + x^2 - x^3) / (1 - 3*x^2 - 2*x^3 - x^4 + x^5). - Colin Barker, Jan 08 2019

A264492 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

12, 16, 212, 788, 4772, 23076, 122628, 626276, 3250500, 16761124, 86652932, 447525860, 2312212676, 11944531620, 61707373956, 318782647652, 1646858513988, 8507781990436, 43951835558660, 227058335082212, 1172999888706500
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Examples

			Some solutions for n=4:
..5..2..7..4..9....1..6.14..8..9....1..6..7..8..9....1..6..7..8..9
..0..1.12.13.14...10.11..2.13..4...10.11..2.13..4...10.18..2.13..4
.22.16.17..8..3....5..0.17.18..3....5..0.24.18..3...15..0.17.14..3
.20.21..6.23.24...20.21.22..7.24...20.21.22.23.14...20..5.22.23.24
.15.10.11.18.19...15.16.23.12.19...15.16.17.12.19...21.16.11.12.19

Links

Crossrefs

Row 4 of A264490.

Formula

Empirical: a(n) = a(n-1) + 16*a(n-2) + 24*a(n-3) + 16*a(n-4) + 32*a(n-5) + 32*a(n-6).
Empirical g.f.: 4*x*(3 + x + x^2 + 8*x^3 + 4*x^4 - 8*x^5) / ((1 + 2*x)*(1 - 3*x - 10*x^2 - 4*x^3 - 8*x^4 - 16*x^5)). - Colin Barker, Jan 08 2019

A264493 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

25, 214, 2144, 21466, 217049, 2186741, 22085009, 222909614, 2250209521, 22715274695, 229303673852, 2314753967333, 23366787607444, 235881036497193, 2381151813460341, 24037049548970144, 242647163940788960
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 5 of A264490.

Examples

			Some solutions for n=4
..5..2..7..4..9....5..6..7..8..9....5..2..7..4..9....5..6..3..4..9
.10..1.12.13.14...10..1..2.13..4...10.11.12..3.14....0..1..2.13.14
.15..0.17..8..3...11..0.17.18..3...15..0..1..8.19...15.16..7.18.19
..6.11.22.19.24...16.21.22.23.14...20.21..6.13.24...20.21.12.23..8
.25.26.27.28.29...25.26.27.12.29...25.22.17.28.29...25.10.11.28.29
.20.21.16.23.18...20.15.28.19.24...26.27.16.23.18...26.27.22.17.24

Links

Crossrefs

Cf. A264490.

Formula

Empirical: a(n) = 9*a(n-1) +21*a(n-2) -80*a(n-3) -182*a(n-4) -513*a(n-5) +3147*a(n-6) -4670*a(n-7) +1792*a(n-8) +11993*a(n-9) -146379*a(n-10) +645596*a(n-11) -974550*a(n-12) +1347007*a(n-13) -1796051*a(n-14) +2021604*a(n-15) -1643602*a(n-16) +6416137*a(n-17) -8186591*a(n-18) +2810654*a(n-19) -5561728*a(n-20) +19323239*a(n-21) +3115427*a(n-22) +6590912*a(n-23) -60221446*a(n-24) -58598523*a(n-25) -1723783*a(n-26) +55826390*a(n-27) +20203727*a(n-28) -1150476*a(n-29) -852256*a(n-30) -1208160*a(n-31) -4333696*a(n-32) +5792064*a(n-33) +8416768*a(n-34) +2727936*a(n-35) -1180672*a(n-36) -1169408*a(n-37) -414720*a(n-38) -102400*a(n-39)

A264494 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

52, 324, 9714, 142352, 2517024, 42169152, 714303376, 12077450784, 204161943712, 3452345816640, 58366975597504, 986868844185984, 16685367542010496, 282109578735300864, 4769776075129487104, 80645235669257971200
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 6 of A264490.

Examples

			Some solutions for n=4
..5..2..7..4..9....1..6.14..8..9...12.13.14..8..9...12..2..7..4..9
.10..1.12.13.14...10..7..2.13..4....0.11..2..3..4...10.11..8.13.14
.15..0.17..8..3....5..0.17.18..3...15.16..1.18.19...15..0..1.18..3
.20.28..6.19.24...16.21.12.23.24...10..5..6..7.24...20..5..6.19.24
.21.26.11.18.29...15.26.11.28.19...21.26.27.28.29...25.26.27.28.29
.30.31.16.33.34...30.31.32.33.34...30.31.32.17.34...30.31.16.17.34
.25.32.27.22.23...25.20.27.22.29...25.20.33.22.23...21.32.33.22.23

Links

Crossrefs

Cf. A264490.

Formula

Empirical: a(n) = 6*a(n-1) +154*a(n-2) +612*a(n-3) -744*a(n-4) -12624*a(n-5) -45792*a(n-6) -7488*a(n-7) +66816*a(n-8) +235008*a(n-9) -995328*a(n-10) for n>11

A264495 Number of (7+1)X(n+1) arrays of permutations of 0..n*8+7 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.

Original entry on oeis.org

121, 2960, 92052, 2870927, 89130069, 2775259622, 86190450233, 2677639248483, 83164917517453, 2583078930390035, 80227727864116428, 2491794046923957866, 77392440292663757309, 2403726490469501987884, 74657152069390240763825
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 7 of A264490.

Examples

			Some solutions for n=3
..4..5..3..7....4..5..3..7....4..5..6..7....4..5..6..7....4..2..6..7
..0..6.10.11....0..1.10.11....8..9.10..3....0..9..2..3....0..1.10..3
.12..2..1.15...12.13..6..2...12..0..1..2...12.13..1.15...12.13.11.15
..8..9.18.19...16.17.18.19...22.17.18.11...16.14.18.11....8.17..5.19
.17.21.14.23....9..8.22.15...26.13.14.23...20..8.19.10...20.18..9.23
.16.25.13.27...24.25.26.14...16.25.15.19...24.17.26.27...16.25.26.14
.28.29.30.31...28.21.30.31...28.29.30.31...28.29.30.31...28.29.27.31
.24.20.26.22...29.20.23.27...24.20.21.27...21.25.23.22...24.30.21.22

Links

Crossrefs

Cf. A264490.
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