A264520 -id:A264520 - cp's OEIS frontend

A264514 Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

1, 3, 12, 46, 177, 684, 2640, 10180, 39249, 151326, 583444, 2249491, 8673001, 33439105, 128925825, 497078745, 1916507251, 7389171396, 28489249854, 109841457681, 423498192724, 1632814449360, 6295382298780, 24272101648369

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

			Some solutions for n=3:
..5..4..0....3..4..0....3..4..5....3..4..0....5..4..0....3..4..5....3..4..0
..8..1..2....8..1..2....0..1..2....6..1..2....8..1..2....0..1..2....8..1..2
..3.10..6...11.10..5....9.10.11....9.10..5....3.10.11....9.10..6....9.10..5
.14..7..9....6..7.14....6..7..8...14..7..8....6..7.14...14..7..8....6..7.14
.17.16.11....9.16.17...15.16.17...17.16.11....9.16.17...17.16.11...17.16.11
.12.13.15...12.13.15...12.13.14...12.13.15...12.13.15...12.13.15...12.13.15

R. H. Hardin, Table of n, a(n) for n = 1..105

Column 2 of A264520 (nonzero terms only).

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 13*a(n-3) - 11*a(n-4) + 6*a(n-5) - a(n-6).

Empirical g.f.: x*(1 - 3*x + 5*x^2 - 6*x^3 + 5*x^4 - x^5) / (1 - 6*x + 11*x^2 - 13*x^3 + 11*x^4 - 6*x^5 + x^6). - Colin Barker, Jan 08 2019

A264515 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

1, 1, 9, 36, 144, 576, 2116, 8281, 31329, 121801, 467856, 1809025, 6969600, 26884225, 103632400, 399560121, 1540484001, 5939322489, 22899558276, 88289802496, 340406901136, 1312449766884, 5060209759081, 19509827162049, 75220946346001

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Column 3 of A264520.

			Some solutions for n=4
..4..5..0..7....4..5..0..1....4..5..6..7....6..5..0..1....4..7..0..1
..8..1..2..3....8.11..2..3....0..1..2..3...10.11..2..3...10.11..2..3
.14.15..6..9...14.15..6..7...14.15..8..9....4.15..8..7...14..5..6..9
.18.19.10.11...18..9.10.19...18.19.10.11...16..9.18.19....8.17.18.19
.12.13.16.17...12.13.16.17...12.13.16.17...12.13.14.17...12.13.16.15

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

Cf. A264520.

Empirical: a(n) = 3*a(n-1) +7*a(n-2) -17*a(n-3) -5*a(n-4) +60*a(n-5) +8*a(n-6) -24*a(n-7) -36*a(n-8) +36*a(n-11) +24*a(n-12) -8*a(n-13) -60*a(n-14) +5*a(n-15) +17*a(n-16) -7*a(n-17) -3*a(n-18) +a(n-19)

A264516 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

2, 2, 42, 228, 1644, 10368, 65182, 414414, 2603670, 16540506, 104489208, 662121980, 4188014160, 26506383680, 167699955140, 1061128778004, 6714156638826, 42483540261942, 268814679252084, 1700917160828256, 10762539724166324

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Column 4 of A264520.

			Some solutions for n=4
..5..6..0..8..9....7..8..0..1..2....7..6..9..1..2....7..8..0..1..2
.12..1..2..3..4...12.13.14..3..4....0.13..5..3..4...12.11.14..3..4
.17.18..7.11.19....5..6.19.18..9...17.18.10..8.12....5..6.19.18..9
.10.23.24.13.14...10.11.24.23.17...22.11.24.23.14...10.23.24.13.17
.15.16.20.21.22...15.16.20.21.22...15.16.20.21.19...15.16.20.21.22

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 84

Cf. A264520.

Empirical recurrence of order 84 (see link above)

A264517 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

4, 4, 196, 1444, 18769, 186624, 2007889, 20738916, 216384100, 2246191236, 23336228644, 242343536656, 2516566604161, 26133852688384, 271375312681729, 2818084749524496, 29263464821074276, 303881662686399876

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Column 5 of A264520.

			Some solutions for n=4
..8..7.10..1..2..3....8..9.10..1..2..3....8..9..0..1..2..3....8..9..0.11..2..3
..0.13.16.17..4..5....0.13..6.15..4..5...14.15..6.17..4..5...14..1.16..7..4..5
..6.21.20..9.14.11...20..7.12.21.14.11...20..7.22.23.10.11....6.21.12.23.10.15
.12.27.26.15.28.29...26.27.28.29.16.17...12.13.28.29.16.21...24.13.26.29.28.17
.18.19.24.25.22.23...18.19.24.25.22.23...18.19.24.25.26.27...18.19.20.25.22.27

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 90

Cf. A264520.

Empirical recurrence of order 90 (see link above)

A264518 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

6, 8, 644, 8018, 169195, 2856816, 50099452, 868998834, 14882827790, 256959272592, 4398347029348, 75624723708092, 1295898634983579, 22241860959497984, 381337803827858013, 6540985297761847920, 112164265361793394334

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Column 6 of A264520.

			Some solutions for n=4
..9..8..0.12..2..3.13....9..8.11.12..2..3..4....9.10..0..1.13.12..4
.16..1.18.17..4..5..6....0..1.16.17.20..5..6...16.15..2..3.20..5..6
..7.24.23.10.11.26.27....7.24.14.10.25.26.13....7..8.14.24.11.17.18
.14.15.30.33.34.19.20...28.15.32.33.18.19.34...30.31.32.33.23.19.34
.21.22.28.29.25.31.32...21.22.23.29.30.31.27...21.22.28.29.25.26.27

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

Cf. A264520.

A264519 Number of (n+1) X (7+1) arrays of permutations of 0..n*8+7 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

9, 16, 2116, 44521, 1525225, 43731769, 1250046736, 36412654041, 1023636039001, 29395568245824, 828988131959716, 23599139118132769, 667319223491080281, 18929485248132797584, 535857588485957276361, 15182115680784904368400

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Column 7 of A264520.

			Some solutions for n=4
.10..9..0.13.14..3..4.15....8.11..0..1.12..3.14..5....8..9.10.11..2.13..4..5
.18..1..2.19.22..5..6..7...18.17..2.19..4.21..6..7....0..1.18..3.22.23..6..7
..8.27.26.11.12.29.20.21...26..9.10.27.30.13.20.15...26.27.28.29.12.31.14.15
.16.17.34.37.36.39.38.23...16.35.34.37.38.39.22.23...16.17.36.19.20.21.38.39
.24.25.32.33.28.35.30.31...24.25.32.33.28.29.36.31...24.25.32.33.34.35.30.37

R. H. Hardin, Table of n, a(n) for n = 1..129

Cf. A264520.

A264521 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

1, 3, 9, 42, 196, 644, 2116, 6854, 22201, 78076, 274576, 937960, 3204100, 10890360, 37015056, 126620208, 433139344, 1480295124, 5059050129, 17273618712, 58979036736, 201463380504, 688168134481, 2350844113032, 8030694487104

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Row 3 of A264520.

			Some solutions for n=4
..5..6..9..1..2....7..6..0..1..2....7..8..0..1..9....5..6..7..1..2
..0.13.14..3..4...12.13.14..3..4...12.13..2..3..4....0.13.12..3..4
.15.18..7..8.19....5.18.19..8..9....5..6.17.18.19...17.18.19..8..9
.10.11.12.16.17...10.11.15.16.17...10.11.15.16.14...10.11.15.16.14

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

Cf. A264520.

A264522 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

0, 0, 36, 228, 1444, 8018, 44521, 258264, 1498176, 8784648, 51509329, 298721094, 1732390884, 10048882704, 58289410624, 338365016544, 1964179826064, 11397166993164, 66132140115889, 383699043436626, 2226223976362884

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Row 4 of A264520.

			Some solutions for n=4
..7..6..0..1..9....7..8..9..1..2....7..6..9..8..2....5..6..9..1..2
.12.11..2..3..4....0.13.14..3..4....0..1.14..3..4....0.11.12..3..4
..5.18.10..8.19....5..6.19.11.12....5.18.10.11.12...17.18..7..8.19
.20.23.24.13.14...10.21.24.23.17...20.23.22.13.24...10.23.24.13.14
.15.16.17.21.22...15.16.20.18.22...15.16.17.21.19...15.16.20.21.22

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

Cf. A264520.

A264523 Number of (5+1) X (n+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

1, 12, 144, 1644, 18769, 169195, 1525225, 14158040, 131423296, 1263160840, 12140734225, 114747871035, 1084536870921, 10220222182842, 96311102247684, 909854806065252, 8595434470172356, 81152480791177280, 766188743735526400

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Row 5 of A264520.

			Some solutions for n=4
..7..6..0..1..2....5..6..7..1..9....5..6..7..1..9....7..6..0..8..2
.10.13..5..3..4....0.13..2..3..4....0.13..2..3..4...12..1..5..3..4
.15.16.19..8..9...17.18.19..8.12...17.18.19..8.12...15.16.17.11..9
.22.11.12.23.14...10.11.22.23.14...10.11.15.23.14...10.23.22.13.14
.27.28.17.18.29...15.16.27.28.29...25.16.27.28.29...27.28.29.18.19
.20.21.25.26.24...20.21.25.26.24...20.21.22.26.24...20.21.25.26.24

R. H. Hardin, Table of n, a(n) for n = 1..63

Cf. A264520.

A264524 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

Original entry on oeis.org

0, 0, 576, 10368, 186624, 2856816, 43731769, 696507612, 11093144976, 178795599948, 2881767670929, 45735094197492, 725838818428816, 11506986415823456, 182424435028933696, 2894261482434465920

Offset: 1

R. H. Hardin, Nov 16 2015

nonn

Row 6 of A264520.

			Some solutions for n=4
..7..6..0..1..2....7..6..9..1..2....7..8..9..1..2....5..8..7..1..2
.12.13..5..3..4....0.13..5..3..4....0.11.14..3..4....0.13.14..3..4
.15.18.17..8..9...15.16.10..8.12....5..6.19.18.12...15..6.10.11..9
.10.11.24.16.14...20.11.22.23.14...10.23.22.13.17...22.23.12.16.17
.27.28.20.21.19...27.28.17.18.19...15.16.20.21.29...27.28.20.18.19
.32.33.22.23.34...32.21.34.33.24...30.31.34.33.24...32.21.34.33.24
.25.26.30.31.29...25.26.30.31.29...25.26.27.28.32...25.26.30.31.29

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A264520.

cp's OEIS Frontend

A264514 Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264515 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264516 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264517 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264518 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264519 Number of (n+1) X (7+1) arrays of permutations of 0..n*8+7 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264521 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264522 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264523 Number of (5+1) X (n+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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A264524 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

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