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

A264471 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

0, 4, 6, 16, 49, 124, 384, 1041, 2868, 8189, 22760, 63910, 179095, 500979, 1405340, 3935526, 11024880, 30892270, 86537090, 242454683, 679254490, 1902958308, 5331384633, 14936238820, 41845207329, 117233159460, 328438385380
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 3 of A264476.

Examples

			Some solutions for n=4
..5..0..1..2....5..6..7..2....5..0..7..2....5..6..7..2....5..6..7..2
..9..4.11..3....0..4.11..3....9..1.11..3....0..1.11..3....9..4.11..3
.13.14.15..7...13..8..1.10...13.14.15.10...13..8.15.10...13..0..1.10
..8.18.19..6...17.18.19.14....8..4.19..6...17..4.19.14....8.18.19.14
.12.16.17.10...12.16..9.15...12.16.17.18...12.16..9.18...12.16.17.15

Links

Crossrefs

Cf. A264476.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +6*a(n-3) -6*a(n-4) +6*a(n-5) -27*a(n-6) +5*a(n-7) -9*a(n-8) +33*a(n-9) -4*a(n-10) +7*a(n-11) -12*a(n-12) +a(n-13) -a(n-14) +a(n-15)

A264472 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

0, 8, 16, 120, 456, 2232, 10116, 45792, 212112, 960336, 4418388, 20134008, 92208780, 421315344, 1926779076, 8809428456, 40277366640, 184164908040, 842016117672, 3849965354232, 17602701446772, 80483933441520, 367989633268848
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Examples

			Some solutions for n=4:
..6..0..8..9..3....6..7..1..2..3....6..7..8..2..3....6..7..1..2..3
.11..5..2..7..4....0..5.13.14..4....0..1.13.14..4....0..5.13.14..4
.16.10..1.12.13...16.10.11.12..9...16.17.11.19..9...16.10.11.19..9
.21.22.23.24.14...21.22.23.24..8...10..5.12.24.18...21.22.12.24..8
.15.20.17.18.19...15.20.17.18.19...15.20.21.22.23...15.20.17.18.23

Links

Crossrefs

Column 4 of A264476.

Formula

Empirical: a(n) = 18*a(n-2) + 36*a(n-3) - 45*a(n-4) - 216*a(n-5) - 243*a(n-6) for n>7.
Empirical g.f.: 4*x^2*(2 + 4*x - 6*x^2 - 30*x^3 - 36*x^4 + 9*x^5) / ((1 - 3*x^2 - 9*x^3)*(1 - 15*x^2 - 27*x^3)). - Colin Barker, Jan 08 2019

A264473 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

1, 17, 57, 456, 3540, 24773, 174927, 1262270, 8905776, 63373156, 449506816, 3184860720, 22596207841, 160137303788, 1135302681211, 8048142435691, 57049038241053, 404414221946254, 2866733296182372, 20321383697508618
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 5 of A264476.

Examples

			Some solutions for n=4
..7..0..1.10.11..4....7..8..1.10..3..4....7..0..1.10.11..4....7..0..9.10..3..4
.13..6..2..3..9..5....0..6..2.16.17..5...13.14..2..3.17..5...13.14.15..8.17..5
.19.12..8.22.23.16...19.12.21..9.23.11...19.20.21..9.23.16....6.20..1..2.23.11
.25.26.14.15.29.17...25.13.14.15.29.22...12..6.27..8.29.22...12.26.19.28.29.22
.18.24.20.21.27.28...18.24.20.26.27.28...18.24.25.26.15.28...18.24.25.21.27.16

Links

Crossrefs

Cf. A264476.

Formula

Empirical recurrence of order 84 (see link above)

A264474 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

0, 36, 160, 2272, 28489, 310748, 3842048, 43644384, 505769648, 5849013488, 67135006848, 774054696448, 8896767499776, 102334987567872, 1176757087435008, 13529311221840896, 155560070455705600, 1788454272171147264
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 6 of A264476.

Examples

			Some solutions for n=4
..8..0.10..2..3.13..5....8..9.10..2..3.13..5....8..0..1.11.12..4..5
.15..1.17..9..4.20..6....0..1.17.18..4.20..6...15.16..2.18.10.20..6
..7.23.24.25.11.12.19...22.14.15.25.11.27.19....7.23..9.25..3.27.13
.14.30.22.32.33.34.26...29..7.16.32.24.34.12...14.30.22.17.33.34.26
.21.28.29.16.31.18.27...21.28.23.30.31.26.33...21.28.29.24.31.32.19

Links

Crossrefs

Cf. A264476.

Formula

Empirical: a(n) = 12*a(n-1) +48*a(n-2) -400*a(n-3) -4048*a(n-4) +11008*a(n-5) +78144*a(n-6) +130560*a(n-7) -1737728*a(n-8) +404992*a(n-9) -2965248*a(n-10) +63133696*a(n-11) -237834240*a(n-12) +595820544*a(n-13) -2770386944*a(n-14) +13195608064*a(n-15) -29207560192*a(n-16) +119052697600*a(n-17) -486106202112*a(n-18) +1221473599488*a(n-19) -4705283473408*a(n-20) +13249705672704*a(n-21) -32820932116480*a(n-22) +110719425052672*a(n-23) -236031269928960*a(n-24) +531386238763008*a(n-25) -1555418111279104*a(n-26) +2696466367774720*a(n-27) -5226184925249536*a(n-28) +13099581533323264*a(n-29) -18769762997764096*a(n-30) +29251407345352704*a(n-31) -60587488736968704*a(n-32) +67342888178024448*a(n-33) -70931694131085312*a(n-34) +112589990684262400*a(n-35) -72057594037927936*a(n-36) for n>40

A264475 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

0, 76, 484, 11044, 215607, 4039259, 74367790, 1358980008, 25131223920, 454913826610, 8308148502158, 150817534124764, 2737572458162063, 49698482940927931, 901239835437298103, 16348456871339244625
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Column 7 of A264476.

Examples

			Some solutions for n=4
..9..0.11.12..3..4.15..6....9..0..1.12.13.14..5..6....9..0.11.12.13.14.15..6
.17..8..2.10.21..5.13..7...17.18..2..3..4.22.23..7...17..1..2..3..4..5.23..7
.25.26..1.18.19.20.14.22...25.26.10.11.19.20.21.15...25.16.27.18.29.20.31.22
.16.34.35.36.37.38.39.23...16..8.35.36.27.38.39.30...33..8.35.10.37.28.39.30
.24.32.33.27.28.29.30.31...24.32.33.34.28.29.37.31...24.32.26.34.19.36.21.38

Links

Crossrefs

Cf. A264476.

A264477 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

0, 4, 6, 16, 57, 160, 484, 1449, 4250, 12736, 37980, 112684, 335528, 998929, 2971856, 8844112, 26318889, 78319204, 233069764, 693574740, 2063954658, 6142018600, 18277651737, 54391278960, 161859683044, 481668191001, 1433366397054
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 3 of A264476.

Examples

			Some solutions for n=4
..6..0..1..9..3....6..7..8..9..3....6..0..8..9..3....6..0..1..2..3
.11..5..2.14..4...11.12..2.14..4...11..5..2.14..4...11.12.13.14..4
.16.17.18.19.13....5..0..1.19.13...16.17..1.19.13....5.17.18.19..9
.10.15.12..7..8...10.15.16.17.18...10.15.12..7.18...10.15.16..7..8

Links

Crossrefs

Cf. A264476.

Formula

Empirical: a(n) = 2*a(n-1) +10*a(n-3) -4*a(n-4) +8*a(n-5) -25*a(n-6) -4*a(n-8) +33*a(n-9) +4*a(n-10) -4*a(n-11) -10*a(n-12) -2*a(n-13) +a(n-15)

A264478 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

1, 8, 16, 120, 456, 2272, 11044, 49200, 236196, 1113296, 5157772, 24352896, 114256032, 534574312, 2511482164, 11778946872, 55224573264, 259130295272, 1215413555584, 5700599522328, 26741489475588, 125432405841016
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Examples

			Some solutions for n=4:
..6..7..8..9..3....6..7..1..9..3....6..7..1..2..3....6..7..1..2..3
..0.12..2.14..4....0.12..2.14..4....0.12.13.14..4....0..5.13.14..4
..5.10..1.19.13....5.17.18.19.13....5.10.11.19..9...16.17.18.19..9
.21.11.16.24.18...10.11.16.24..8...21.22.16.24..8...10.11.12.24..8
.15.20.17.22.23...15.20.21.22.23...15.20.17.18.23...15.20.21.22.23

Links

Crossrefs

Row 4 of A264476.

Formula

Empirical: a(n) = 9*a(n-2) + 54*a(n-3) + 60*a(n-4) - 54*a(n-5) - 279*a(n-6) - 270*a(n-7) + 64*a(n-8) - 864*a(n-9) - 1728*a(n-10) for n>11.
Empirical g.f.: x*(1 + 8*x + 7*x^2 - 6*x^3 - 180*x^4 - 98*x^5 + 211*x^6 + 294*x^7 - 208*x^8 + 576*x^9 + 2496*x^10) / (1 - 9*x^2 - 54*x^3 - 60*x^4 + 54*x^5 + 279*x^6 + 270*x^7 - 64*x^8 + 864*x^9 + 1728*x^10). - Colin Barker, Jan 08 2019

A264479 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

1, 16, 49, 456, 3540, 28489, 215607, 1711113, 13390929, 103239049, 808268548, 6305839174, 49028148726, 382311026201, 2980060222502, 23211745902165, 180884486207033, 1409598089228359, 10983040186007341, 85581889782163761
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 5 of A264476.

Examples

			Some solutions for n=4
..6..0..1..9..3....6..7..1..9..3....6..7..1..9..3....6..7..1..2..3
.11..5..2.14..4....0.12..2.14..4....0.12..2.14..4...11.12.13.14..4
.16.10..7..8.13....5.17.18.19.13....5.17.11.19.13....5..0.18.19..9
.21.22.12.24.18...21.15.16.24..8...21.15.16.24..8...10.15.16.24..8
.15.27.17.29.19...26.10.11.29.23...26.10.28.29.23...26.27.21.29.23
.20.25.26.23.28...20.25.22.27.28...20.25.22.27.18...20.25.22.17.28

Links

Crossrefs

Cf. A264476.

Formula

Empirical recurrence of order 84 (see link above)

A264480 Number of (6+1)X(n+1) arrays of permutations of 0..n*7+6 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

1, 32, 124, 2232, 24773, 310748, 4039259, 50217832, 620351086, 7791932046, 96985215280, 1205278291192, 15033721660535, 187188468194402, 2330142431854154, 29024775202912332, 361434709901725109
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 6 of A264476.

Examples

			Some solutions for n=4
..6..7..8..9..3....6..0..1..2..3....6..0..8..9..3....6..0..8..2..3
..0..1..2.14..4...11.12.13.14..4...11..1..2.14..4...11..1.13..7..4
..5.17.11.19.13....5.10..7..8..9...16.10..7.19.13....5.17.18.19..9
.10.22.12.24.18...21.15.23.17.18...21..5.12.24.18...10.22.16.24.14
.26.27.21.29.23...26.27.28.29.19...26.27.17.22.23...26.27.21.12.23
.20.15.16.34.28...20.32.16.34.24...20.15.33.34.28...20.15.33.34.28
.25.30.31.32.33...25.30.31.22.33...25.30.31.32.29...25.30.31.32.29

Links

Crossrefs

Cf. A264476.

A264481 Number of (7+1)X(n+1) arrays of permutations of 0..n*8+7 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

Original entry on oeis.org

2, 64, 384, 10116, 174927, 3842048, 74367790, 1462247321, 29509300516, 577847245296, 11385134340072, 225727859320572, 4442739834521648, 87589711996716421, 1729226298092553854, 34086490092213796815
Offset: 1

Views

Author

R. H. Hardin, Nov 14 2015

Keywords

Comments

Row 7 of A264476.

Examples

			Some solutions for n=4
..6..0..1..2..3....6..7..8..2..3....6..0..1..9..3....6..7..1..9..3
.11.12.13..7..4....0..1.13.14..4...11.12..2..7..4....0.12..2.14..4
..5.10.18..8..9...16.10.11.19..9....5.10.18..8.13....5.17.11..8.13
.21.15.23.24.14...21..5.12.24.18...21.22.23.24.14...10.22.16.24.18
.26.16.17.29.19...15.20.17.22.23...15.16.17.29.19...15.27.21.29.19
.20.25.22.34.28...31.32.26.27.28...31.32.26.27.28...20.25.26.34.28
.36.37.31.39.33...25.37.38.39.29...25.20.38.39.33...36.37.31.39.23
.30.35.32.27.38...30.35.36.33.34...30.35.36.37.34...30.35.32.33.38

Links

Crossrefs

Cf. A264476.
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