A264071 -id:A264071 - cp's OEIS frontend

A264067 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

34, 605, 12100, 239580, 4745620, 94000060, 1861931060, 36880691100, 730524027860, 14470047586940, 286619288597620, 5677287244745820, 112454366267732500, 2227469555002850620, 44121191405337881780, 873942149581465363740, 17310839904533248019540, 342889032579435158191100

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=3:
..0..1..8..9..4....6..8..9..3..4....6..1..8..9..4....0..8..9..3..4
..5..6.14..2..3...12..0.14..1..2...11..0..7..2..3....5..6.13..1..2
.16.17.12.13..7...16..5.18.13..7...10..5.18.19.14...17.11.19..7.14
.15.10.11.18.19...15.10.17.11.19...15.16.17.12.13...15.16.10.18.12

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

Column 4 of A264071.

Empirical: a(n) = 19*a(n-1) +16*a(n-2) for n>3.

Empirical g.f.: x*(34 - 41*x + 61*x^2) / (1 - 19*x - 16*x^2). - Colin Barker, Jan 04 2019

A264068 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

89, 3025, 131890, 5645376, 242621698, 10427064769, 448121165789, 19258783041289, 827679549612058, 35570961850254336, 1528723680011326810, 65699547278636775625, 2823551809301370027485, 121347028252680274383361, 5215098663055950428459458, 224127895483153188149350464

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=3:
..0..8.10..3.11..5....8..1..2.10..4..5....0..8..2..3.11..5....7..1.10..3.11..5
.13.15..1..2.17..4....6.15..0.16..3.11...14..7..1..9.10..4....6..0.15..2.17..4
.12..6.22..7.16..9...19.13.21..7..9.17...20.21..6.15.23.17...19.13.22..8.16..9
.18.19.20.21.14.23...18.12.20.14.22.23...18.19.12.13.22.16...18.12.20.21.14.23

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

Column 5 of A264071.

Empirical: a(n) = 43*a(n-1) - 43*a(n-3) + a(n-4) for n>5.

Empirical g.f.: x*(89 - 802*x + 1815*x^2 - 22067*x^3 + 516*x^4) / ((1 - x)*(1 + x)*(1 - 43*x + x^2)). - Colin Barker, Jan 04 2019

A264069 Number of (n+1) X (6+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

233, 15125, 1445345, 130697424, 11909009849, 1084282319384, 98725402363225, 8989061417123964, 818464496640651553, 74522143720797473932, 6785327805998071795553, 617811983591878946983992, 56252499213505961292639449, 5121855437908705959886793744, 466350890958042737691769834681

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=2:
..9..1..2..3..4.13..6....0..1..2..3..4..5..6....8..9..2.12.13..5..6
.15..0.17.18.19.20..5....7.16.18.19.11.12.13...15..0.18..1.19..3..4
.14..7.16..8.10.11.12...14.15..8.17..9.10.20...14..7.16.17.10.11.20

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

Column 6 of A264071.

Empirical: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5) for n > 7.

A264070 Number of (n+1) X (7+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

610, 75625, 15892745, 3057071776, 601052131669, 118020590202856, 23180312098708413, 4552817445649814704, 894213655660356295077, 175631478939257301328632, 34495577433083786070527245, 6775236817617034700050817216, 1330716496160907700646992379893

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=2:
..0..1..2..3.14..5..6..7...10..1..2.12..4..5.15..7....9..1..2..3..4..5..6..7
..8..9.19.20.12.23..4.15....8..0.19.21..3.22.14..6....8..0.10.20.22.23.14.15
.16.17.18.10.11.21.22.13...16.17.18..9.20.11.13.23...16.17.18.19.11.21.12.13

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

Column 7 of A264071.

Empirical: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5) for n > 8.

A264072 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

8, 89, 1210, 12100, 131890, 1445345, 15892745, 174807490, 1922750500, 21148816810, 232621218005, 2558660023205, 28143353265610, 309555910473700, 3404884300976290, 37451189626157945, 411935173248700145, 4530979887509803090, 49837401790945888900, 548174275529004512410

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=4:
..7..1..2..9..4....0..7..9..3..4....0..1..2..3..4....6..1..2..3..4
..5.12..0..8..3....5..6.14..1..2...11.13..7.14..9...12.13..0..8..9
.17.18.19..6.14...17.11.18.13..8...16..5.18..6..8...10.17..5..7.14
.15.16.10.11.13...15.16.10.12.19...15.10.17.12.19...15.16.11.18.19

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

Row 3 of A264071.

Empirical: a(n) = 12*a(n-1) - 12*a(n-2) + 12*a(n-3) - 12*a(n-4) + a(n-5) for n>7.

Empirical g.f.: x*(8 - 7*x + 238*x^2 - 1448*x^3 + 238*x^4 - 5595*x^5 + 516*x^6) / ((1 - x)*(1 - 11*x + x^2 - 11*x^3 + x^4)). - Colin Barker, Jan 04 2019

A264073 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

16, 377, 12100, 239580, 5645376, 130697424, 3057071776, 70815364224, 1640245587376, 37991496430624, 879962725844576, 20381782810954224, 472084850498355776, 10934475563176382624, 253265394378463623376, 5866157880096665663424, 135872523597900600539776

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=3:
..5..1..7..3....0..1..7..3....0..6..2..3....5..6..7..3....0..1..7..3
..4..0..6..2...10..5.11..2....4.11..1..7....4..0..1..2....4.10..6..2
.13..9.15.11....8.15..4..6...14..9.15..5....8..9.10.11...14..9..5.11
.17..8.14.10...17.18.14..9...17.18..8.10...18.13.14.15...18..8.19.15
.16.12.18.19...16.12.13.19...16.12.13.19...16.17.12.19...16.17.12.13

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

Row 4 of A264071.

Empirical: a(n) = 24*a(n-1) -19*a(n-2) -11*a(n-3) +36*a(n-4) +3*a(n-5) for n > 9.

A264074 Number of (5+1) X (n+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

32, 1597, 121000, 4745620, 242621698, 11909009849, 601052131669, 29725091157674, 1480480693010264, 73724395135813664, 3672334488630561424, 182928020836836645194, 9112104813964559988449, 453896950263615921209389, 22609753301495146547501389, 1126248909020070779347948049

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=3:
..0..1..2..3....5..1..7..3....0..1..2..3....5..1..7..3....0..7..2..3
..4..5..6..7....4..0..6..2....9..5.11..7....4..0..6..2....4.11..6..1
..8..9.10.11...14.15.10.11....8..4.10..6....8.14.10.11....8.14.10..5
.17.19.14.15...12.19..8..9...12.13.19.15...12.19..9.15...12.19..9.15
.16.12.18.13...22.17.23.13...21.22.18.14...21.22.23.13...16.17.18.13
.20.21.22.23...20.21.16.18...20.16.17.23...20.16.17.18...20.21.22.23

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

Row 5 of A264071.

Empirical: a(n) = 55*a(n-1) -257*a(n-2) -66*a(n-3) -558*a(n-4) +20414*a(n-5) -105459*a(n-6) +187369*a(n-7) -105459*a(n-8) +20414*a(n-9) -558*a(n-10) -66*a(n-11) -257*a(n-12) +55*a(n-13) -a(n-14) for n > 19.

A264075 Number of (6+1) X (n+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

64, 6765, 1210000, 94000060, 10427064769, 1084282319384, 118020590202856, 12417526726851620, 1326024276162241425, 141133437011428928000, 15037363809591528083800, 1601021055218612828398400, 170459414939407294713069200, 18148606785812097702853499600

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=2:
..0..5..2....0..5..2....0..1..2....0..5..2....4..5..2....0..5..2....0..1..2
..8..4..1....8..4..1....3..8..5....3..8..1....8..0..1....7..8..1....8..4..5
..6.11..3...10.11..3...11..7..4...10..7..4....6.11..3...11..3..4...11..7..3
..9.10..7...14..6..7...13.14..6....9..6.11...14.10..7....9.14..6...13.14..6
.17.13.14...12.13..9...12..9.10...12.17.14...12.17..9...17.13.10...12..9.10
.15.16.12...20.16.17...19.20.17...19.20.13...19.16.13...19.20.12...20.16.17
.18.19.20...18.19.15...18.15.16...18.15.16...18.15.20...18.15.16...18.19.15

R. H. Hardin, Table of n, a(n) for n = 1..152

Row 6 of A264071.

Empirical: a(n) = 119*a(n-1) -1238*a(n-2) -11504*a(n-3) +132848*a(n-4) +180912*a(n-5) -203520*a(n-6) +1542400*a(n-7) +2403200*a(n-8) -768000*a(n-9) +640000*a(n-10) for n > 19.

A264076 Number of (7+1) X (n+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

128, 28657, 12100000, 1861931060, 448121165789, 98725402363225, 23180312098708413, 5190313095361393549, 1189964170757867345445, 271062838744567222384845, 61955353860458361394198745, 14139394538378320773485110770, 3228834241484744624868474176520

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=2:
..4..5..2....0..1..2....4..5..2....4..5..2....0..5..2....4..5..2....0..5..2
..7..0..1....8..4..5....8..0..1....3..0..1....8..4..1....8..0..1....3..4..1
.11..3..8...10.11..3...10..7..3...11..7..8....6..7..3....6..7..3...10.11..8
.13.14..6....9..6..7....9..6.11...13.10..6...14.10.11...14.10.11...13..6..7
.17..9.10...17.13.14...12.13.14...17..9.14...17.13..9...12.17..9...12..9.14
.20.16.12...15.16.12...20.16.17...15.16.12...15.20.12...15.16.13...15.16.17
.18.23.15...22.23.20...18.19.15...22.23.20...22.23.16...18.23.20...22.19.20
.21.22.19...21.18.19...21.22.23...21.18.19...21.18.19...21.22.19...21.18.23

R. H. Hardin, Table of n, a(n) for n = 1..34

Row 7 of A264071.

A264066 Number of (n+1) X (n+1) arrays of permutations of 0..(n+1)^2-1 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

Original entry on oeis.org

2, 21, 1210, 239580, 242621698, 1084282319384, 23180312098708413, 2169349966829797899136

Offset: 1

R. H. Hardin, Nov 02 2015

nonn

			Some solutions for n=3:
..6..1..7..3....5..1..7..3....6..1..7..3....0..1..2..3....0..6..2..3
.10.11..0..2....9.11..0..2....4..5..0..2...10..5..6..7....4.11..1..7
..8..9..4..5....8.15..4..6...14.15.10.11...13..4.15.11....8.14.15..5
.12.13.14.15...12.13.14.10...12.13..8..9...12..8.14..9...12.13..9.10

Main diagonal of A264071.

cp's OEIS Frontend

A264067 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264068 Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264069 Number of (n+1) X (6+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264070 Number of (n+1) X (7+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264072 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264073 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264074 Number of (5+1) X (n+1) arrays of permutations of 0..n*6+5 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264075 Number of (6+1) X (n+1) arrays of permutations of 0..n*7+6 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264076 Number of (7+1) X (n+1) arrays of permutations of 0..n*8+7 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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A264066 Number of (n+1) X (n+1) arrays of permutations of 0..(n+1)^2-1 with each element having index change +-(.,.) 0,0 1,1 or 1,2.

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