A264341 -id:A264341 - cp's OEIS frontend

A264337 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

181, 3567, 70669, 1399783, 27726581, 549201567, 10878455069, 215477871383, 4268134837381, 84542207852367, 1674592106593069, 33169925350906183, 657022055372706581, 13014137857695923967, 257780972182185860669

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

			Some solutions for n=3:
..0..2..1..4..3....0..8..1..3..4....7..1..3..2..4....0..2..1..4..3
.12..6..7..9..8...12..5..7..9..2....5.13..0..8..9....5..6.14..9..8
.17.10..5.14.13...17.11.13..6.14...11.10.12..6.14...11.10.12.13..7
.16.15.18.11.19...15.16.10.18.19...15.17.16.19.18...16.15.18.17.19

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 4 of A264341.

Empirical: a(n) = 19*a(n-1) + 16*a(n-2).
Conjectures from Colin Barker, Jan 07 2019: (Start)
G.f.: x*(181 + 128*x) / (1 - 19*x - 16*x^2).
a(n) = (2^(-n)*((19-5*sqrt(17))^n*(-21+4*sqrt(17)) + (21+4*sqrt(17))*(19+5*sqrt(17))^n)) / sqrt(17).
(End)

A264338 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

676, 28925, 1243225, 53429620, 2296230561, 98684484373, 4241136597604, 182270189212469, 7833376999538689, 336652940790951028, 14468243077011355641, 621797799370697341405, 26722837129862974324900

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

			Some solutions for n=2:
..8..2..1..3..4..5....0..2..1..4..3..5....0..9..2..4..3..5....0..1.10..3..5..4
..6..7..0.17.11.10...14.15..7.10..9.11....6..8..7..1.11.10....7..6..9..8..2.11
.12.14.13.16.15..9...12.13..6.16..8.17...12.13.14.16.15.17...12.14.13.15.17.16

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 5 of A264341.

Empirical: a(n) = 43*a(n-1) - 43*a(n-3) + a(n-4).

Empirical g.f.: x*(676 - 143*x - 550*x^2 + 13*x^3) / ((1 - x)*(1 + x)*(1 - 43*x + x^2)). - Colin Barker, Jan 07 2019

A264339 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

2521, 223356, 20386617, 1855980772, 168990466353, 15386771913704, 1400983500645217, 127561175981852920, 11614593343457551705, 1057522224021474274212, 96288627697354864622745

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Column 6 of A264341.

			Some solutions for n=1
..9..1..2..3..5..4..6....9..0..3..2.13..6..5....0.10..2.12..3..5..6
..7..8..0.10.11.12.13....8..7.10..1.11.12..4....8..7..9..1.11.13..4

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

Empirical: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5)

A264340 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

9409, 1759250, 345358201, 67833964762, 13323150080401, 2616784941180034, 513959727627375369, 100946240914292115722, 19826735452231888373729, 3894146380641069135233138, 764844826340243559292129305

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Column 7 of A264341.

			Some solutions for n=1
..1..0..3..2..5..4..6..7....0..1..2..3..4..5..7..6....0..2..1..3.14.15..7..6
..8.10..9.11.12.13.15.14....9..8.10.11.12.14.13.15....8.10..9.11.13.12..4..5

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

Empirical: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5)

A264342 Number of (2+1)X(n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

8, 55, 490, 3567, 28925, 223356, 1759250, 13750304, 107777857, 843913133, 6610346674, 51772001513, 405494413096, 3175909815583, 24874462255642, 194822212724279, 1525890963999701, 11951115491689468, 93603785927597586

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 2 of A264341.

			Some solutions for n=4
..0..8..9..4..3....0..2..1..4..3....0..8..1..4..3....0..8..3..2..4
..6..5.14..1..2....6..5.14..9..8....6..5.14..9..2....6..5..7..1..9
.10.11.13.12..7...10.11.13.12..7...10.12.11.13..7...10.11.13.12.14

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

Empirical: a(n) = 6*a(n-1) +26*a(n-2) -72*a(n-3) -195*a(n-4) +284*a(n-5) +555*a(n-6) -424*a(n-7) -555*a(n-8) +284*a(n-9) +195*a(n-10) -72*a(n-11) -26*a(n-12) +6*a(n-13) +a(n-14)

A264343 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

16, 233, 4900, 70669, 1243225, 20386617, 345358201, 5804687049, 97945201592, 1651466105125, 27856916781264, 469861192549345, 7925440297808628, 133682668669239757, 2254906043186042569, 38034843997925237049

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 3 of A264341.

			Some solutions for n=4
..0..2..1..3..4....7..8..3..2..4....1..0..9..3..4....0..8..1..4..3
.12..6..8..7..9....5..6..0..1..9....5..7..6..8..2....5..6.14..9..2
.10.11..5.13.14...17.10.13.12.14...11.12.19.13.14...17.11.13.12..7
.15.17.16.18.19...16.15.18.11.19...15.16.10.17.18...15.16.10.18.19

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

Empirical: a(n) = 14*a(n-1) +139*a(n-2) -1260*a(n-3) -7702*a(n-4) +43762*a(n-5) +217890*a(n-6) -744490*a(n-7) -3383575*a(n-8) +6630690*a(n-9) +29495043*a(n-10) -31906396*a(n-11) -148462702*a(n-12) +80910366*a(n-13) +438178264*a(n-14) -91294992*a(n-15) -756685497*a(n-16) +756685497*a(n-18) +91294992*a(n-19) -438178264*a(n-20) -80910366*a(n-21) +148462702*a(n-22) +31906396*a(n-23) -29495043*a(n-24) -6630690*a(n-25) +3383575*a(n-26) +744490*a(n-27) -217890*a(n-28) -43762*a(n-29) +7702*a(n-30) +1260*a(n-31) -139*a(n-32) -14*a(n-33) +a(n-34).

A264344 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

32, 987, 49000, 1399783, 53429620, 1855980772, 67833964762, 2424688746359, 87826990190824, 3164364890450187, 114329873155945874, 4126859698045051896, 149032951757557392004, 5381261860217202123333, 194318967652718474091224

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 4 of A264341.

			Some solutions for n=3
..1..0..2..3....1..0..3..2....0..7..2..3....1..0..2..3....1..7..2..3
..4..5..6..7....4..6..5..7....5..4..6..1...10..5..7..6....4..5..0..6
..8..9.10.11...14..9.11.10....8..9.10.11....8..9..4.11....8.10..9.11
.12.13.14.15...12.19..8.15...12.13.15.14...13.19.14.15...12.13.14.15
.16.17.18.19...17.16.18.13...17.16.18.19...16.17.12.18...16.17.19.18

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

A264345 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

64, 4181, 490000, 27726581, 2296230561, 168990466353, 13323150080401, 1013466370660345, 78811815228451548, 6076970313680986922, 470875474583958043505, 36443115363342618926880, 2822865567835490612412633

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 5 of A264341.

			Some solutions for n=2
..5..2..1....1..0..2....1..0..2....1..0..2....1..0..2....1..0..2....5..1..2
..4..3..0....3..5..4....8..5..4....3..5..4....4..3..5....3..5..4....3..4..0
..6..7..8....6..7..8....7..6..3...11..8..7...11..8..7...11..8..7....6..7..8
.10..9.11....9.11.10....9.10.11....9.10..6...10..9..6...14.10..6...14.11.10
.12.13.14...13.12.14...17.14.13...17.13.14...13.12.14...12.13..9...12.13..9
.15.17.16...15.17.16...15.16.12...15.16.12...16.15.17...15.17.16...15.17.16

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A264341.

A264346 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

128, 17711, 4900000, 549201567, 98684484373, 15386771913704, 2616784941180034, 423590351890979093, 70720633596543340140, 11667647323281661702544, 1939303748261775631813520, 321550922297722913366223227

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 6 of A264341.

			Some solutions for n=2
..5..2..1....0..1..2....5..2..1....0..2..1....5..2..1....0..1..2....5..1..2
..3..4..0....8..5..4....3..4..0....8..5..4....8..4..0....4..3..5....4..3..0
..7..6..8....7..6..3...11..7..8....7..6..3....7..6..3....6..7..8...11..7..8
.10..9.11...10..9.11...10..9..6....9.10.11....9.11.10...14.10.11...10..9..6
.17.14.13...13.12.14...12.13.14...12.14.13...12.14.13...17.13..9...12.14.13
.15.16.12...20.17.16...20.17.16...16.15.17...20.17.16...16.15.12...15.17.16
.18.19.20...19.18.15...19.18.15...19.18.20...19.18.15...18.20.19...19.18.20

R. H. Hardin, Table of n, a(n) for n = 1..123

Cf. A264341.

A264347 Number of (7+1)X(n+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Original entry on oeis.org

256, 75025, 49000000, 10878455069, 4241136597604, 1400983500645217, 513959727627375369, 177045004728184406986, 63460182455433271780660, 22401940593595999915880850, 7987037973987954760973196580

Offset: 1

R. H. Hardin, Nov 11 2015

nonn

Row 7 of A264341.

			Some solutions for n=2
..1..0..2....0..1..2....0..1..2....5..1..2....0..2..1....5..1..2....0..1..2
..3..4..5....4..3..5....3..4..5....3..4..0....3..4..5....4..3..0....3..4..5
..6..8..7....6..7..8....6..8..7....6..7..8....7..6..8....6..7..8....7..6..8
.10..9.11....9.10.11....9.10.11....9.11.10...10..9.11....9.10.11...14.11.10
.13.12.14...12.13.14...17.13.14...12.13.14...17.13.14...13.12.14...12.13..9
.15.17.16...20.16.17...15.16.12...15.17.16...20.16.12...20.17.16...15.16.17
.23.20.19...18.19.15...23.20.19...18.20.19...23.19.15...23.19.15...18.19.20
.22.21.18...21.23.22...22.21.18...21.22.23...22.21.18...21.22.18...21.23.22

R. H. Hardin, Table of n, a(n) for n = 1..15

Cf. A264341.

cp's OEIS Frontend

A264337 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A264338 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A264339 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A264340 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A264342 Number of (2+1)X(n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A264343 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A264344 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A264345 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A264346 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A264347 Number of (7+1)X(n+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

Views

Author