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 13 results. Next

A264544 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 2, 5, 10, 21, 44, 93, 196, 413, 870, 1833, 3862, 8137, 17144, 36121, 76104, 160345, 337834, 711789, 1499682, 3159709, 6657252, 14026293, 29552268, 62264245, 131185742, 276397777, 582347822, 1226959889, 2585105520, 5446608817
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Examples

			Some solutions for n=4:
..1..2..4....1..2..3....1..2..4....1..2..4....1..3..4....1..2..4....1..3..4
..0..6..7....0..5..6....0..5..7....0..6..7....0..5..2....0..5..7....0..6..2
..3..8..5....7..4..9....3..9.10....3..9..5....7..8.10....3..8.10....7..8..5
.10.12.13...10.12..8....6.12..8...10.12..8....6.12.13....6.12.13...10.12.13
..9.14.11...13.14.11...13.14.11...13.14.11....9.14.11....9.14.11....9.14.11

Links

Crossrefs

Column 2 of A264550.

Formula

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

A264545 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 6, 16, 45, 133, 400, 1204, 3561, 10554, 31493, 93784, 278862, 829809, 2469737, 7349616, 21870896, 65083321, 193678264, 576359005, 1715146434, 5103989104, 15188659597, 45198999981, 134504868528, 400264674436, 1191122820729
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Column 3 of A264550.

Examples

			Some solutions for n=4
..1..2..5..6....1..2..3..5....1..2..3..5....1..4..3..6....1..2..3..5
..0..8..9..3....0..6..7.10....0..8..9.10....0..8..2.10....0..6..7..9
..4.10.12..7....4.12.11.14....4.12..6..7....9..5.12..7....4.10.11.14
.13.14.16.11....8..9.16.18...13.14.16.11...13.14.16.11....8.16.17.18
.17.18.19.15...17.13.19.15...17.18.19.15...17.18.19.15...12.13.19.15

Links

Crossrefs

Cf. A264550.

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)

A264546 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 16, 36, 216, 1160, 4640, 23140, 110592, 501828, 2390752, 11231244, 52348752, 246436064, 1155790856, 5415128884, 25420656744, 119225756880, 559133362408, 2623138509120, 12303725497848, 57710528607716, 270708963027848
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Examples

			Some solutions for n=4:
..1..5..3..6..7....1..2..3..4..7....1..2..3..6..8....1..2..3..7..8
..0.10..2..9..4....0.10..8..9.12....0.10.11.12..4....0.10.11..9..4
.11.12.15..8.18....5..6.15.14.18....5.15..7.17..9....5..6.13.14.18
.16.17.20.13.14...16.11.20.13.23...16.20.18.13.14...16.20.12.21.23
.21.22.23.24.19...21.22.17.24.19...21.22.23.24.19...15.22.17.24.19

Links

Crossrefs

Column 4 of A264550.

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 + 16*x + 27*x^2 + 18*x^3 - 88*x^4 - 154*x^5 + 19*x^6 - 90*x^7 - 628*x^8 - 72*x^9 + 192*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

A264547 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 40, 172, 1528, 14852, 105081, 813473, 6587227, 50597392, 392445418, 3079324224, 23951405053, 186390329980, 1454120420684, 11328848497754, 88249763622117, 687788460643528, 5359344090882789, 41758209474358230, 325395419357215040
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Column 5 of A264550.

Examples

			Some solutions for n=4
..1..2..3..4..8.10....1..2..3..4..9.10....1..6..7..4..5.10....1..6..7..4..9.10
..0.12.13.14.15..5....0..8.13.14.11..5....0.12..2..3.15.16....0..8..2..3.11..5
..6..7.18..9.17.11....6..7.15.20.21.22...13.18..8..9.21.11...13.14.18.19.21.22
.19.24.21.22.16.27...12.24.25.26.16.17...19.24.14.22.27.17...12.20.24.15.16.17
.25.26.20.28.29.23...18.19.27.28.29.23...25.26.20.28.29.23...25.26.27.28.29.23

Links

Crossrefs

Cf. A264550.

Formula

Empirical recurrence of order 84 (see link above)

A264548 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

3, 96, 764, 11728, 163744, 1994830, 25172836, 316806958, 3939510885, 49105816488, 612105030734, 7621730718736, 94917598135688, 1182099712180116, 14720466321079700, 183312321420648794, 2282783100595945090
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Column 6 of A264550.

Examples

			Some solutions for n=4
..1..7..3..4.10..6.12....1..7..3..4.10.11.12....1..2..8..4.10..6.11
..0..9..2.11.16..5.18....0..9..2.16.17..5..6....0.14.15..3.12..5.19
.15..8.17.22.23.20.13...15..8.22.18.23.20.13....7.16..9.18.23.25.13
.14.28.29.25.26.19.32...14.28.29.25.26.19.32...22.28.29.17.26.32.20
.21.30.31.24.33.34.27...21.30.31.24.33.34.27...21.30.31.24.33.34.27

Links

Crossrefs

Cf. A264550.

A264549 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

3, 240, 2728, 66372, 1573479, 29691127, 591482528, 11959837149, 234588752099, 4630258704238, 91650397488268, 1806082543597960, 35618855441537594, 702809886558706588, 13858157412186691169, 273285931814164349815
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Column 7 of A264550.

Examples

			Some solutions for n=4
..1..2..9..4.10..6.12.14....1..2..8..9..5..6.12.13....1..2..3..9.10..6.13.14
..0.16.17..3.13..5.21..7....0.10.16..3..4.20.15..7....0.16.17.12..4..5.15..7
..8.18.24.11.27.22.29.15...17.18.19.11.21.22.14.29....8.18.19.11.21.27.29.30
.25.26.32.19.20.30.37.23...25.32.33.28.35.30.36.23...25.32.33.28.20.35.22.23
.33.34.35.36.28.38.39.31...24.34.26.27.37.38.39.31...24.34.26.36.37.38.39.31

Links

Crossrefs

Cf. A264550.

A264551 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 2, 6, 16, 40, 96, 240, 608, 1536, 3840, 9600, 24064, 60416, 151552, 379904, 952320, 2387968, 5988352, 15015936, 37650432, 94404608, 236716032, 593559552, 1488322560, 3731881984, 9357492224, 23463460864, 58833502208, 147522060288
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Examples

			Some solutions for n=4:
..1..2..6..4..8....1..5..3..4..8....1..5..3..7..8....1..2..5..4..8
..0.10.11..3.13....0.10..2.12.13....0.10..2.12..4....0..7.10..3.12
..5.12..7.14..9...11..6..7.14..9...11..6.13.14..9...11..6.13.14..9

Links

Crossrefs

Row 2 of A264550.

Formula

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

A264552 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

0, 5, 16, 36, 172, 764, 2728, 9880, 38818, 150536, 567680, 2152907, 8249172, 31505782, 119890865, 456906182, 1743546208, 6648727988, 25342679205, 96627142521, 368474752553, 1404944654910, 5356632127953, 20424348993729
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Row 3 of A264550.

Examples

			Some solutions for n=4
..1..2..6..4..8....1..2..3..4..7....1..2..3..6..7....1..2..6..4..8
..0..7.10..3.12....0.10..8..9.13....0.10..8..9..4....0..7.11..3.12
..5.15.13.17..9....5..6.15.17.18....5.15.13.17.18....5.15.13.16..9
.16.11.18.19.14...16.11.12.19.14...16.11.12.19.14...10.17.18.19.14

Links

Crossrefs

Cf. A264550.

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +41*a(n-4) -104*a(n-5) +14*a(n-6) +167*a(n-7) -715*a(n-8) +1169*a(n-9) -1018*a(n-10) -3680*a(n-11) +8691*a(n-12) -10335*a(n-13) +2525*a(n-14) +35277*a(n-15) -50582*a(n-16) +64373*a(n-17) +11060*a(n-18) -207508*a(n-19) +200293*a(n-20) -204582*a(n-21) -124748*a(n-22) +704108*a(n-23) -499827*a(n-24) +365700*a(n-25) +473743*a(n-26) -1541579*a(n-27) +729138*a(n-28) -331526*a(n-29) -929717*a(n-30) +2313138*a(n-31) -591289*a(n-32) +10149*a(n-33) +1058138*a(n-34) -2448606*a(n-35) +225766*a(n-36) +341725*a(n-37) -740229*a(n-38) +1867654*a(n-39) -9921*a(n-40) -441602*a(n-41) +343946*a(n-42) -1047499*a(n-43) -9489*a(n-44) +322880*a(n-45) -125643*a(n-46) +431100*a(n-47) -8968*a(n-48) -160742*a(n-49) +44437*a(n-50) -124400*a(n-51) +6980*a(n-52) +54449*a(n-53) -13758*a(n-54) +23185*a(n-55) -1859*a(n-56) -11695*a(n-57) +2887*a(n-58) -2532*a(n-59) +298*a(n-60) +1457*a(n-61) -383*a(n-62) +155*a(n-63) -26*a(n-64) -100*a(n-65) +29*a(n-66) -4*a(n-67) +a(n-68) +3*a(n-69) -a(n-70)

A264553 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

0, 10, 45, 216, 1528, 11728, 66372, 403920, 2587588, 16422928, 100924052, 627229368, 3931197172, 24518011160, 152485541704, 950191656704, 5926384223020, 36928044675096, 230056295804064, 1433703853124720
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Row 4 of A264550.

Examples

			Some solutions for n=4
..1..2..3..4..7....1..2..3..6..8....1..2..5..6..8....1..5..3..4..7
..0.10.11..9.12....0..7.11..9..4....0..7.10..3..4....0.10..2..9.12
..5..6.15..8.18....5.15.16.14.18...11.12.13.17..9...11..6.13..8.18
.16.17.20.13.14...10.20.12.13.23...16.20.18.21.14...16.17.20.21.14
.21.22.23.24.19...21.22.17.24.19...15.22.23.24.19...15.22.23.24.19

Links

Crossrefs

Cf. A264550.

Formula

Empirical recurrence of order 56 (see link above)

A264554 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

Original entry on oeis.org

1, 21, 133, 1160, 14852, 163744, 1573479, 16103502, 165752029, 1678765742, 16892925020, 170699731951, 1724096806496, 17375168005744, 175086698829941, 1764727636006278, 17783364887589616, 179165583864541771
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2015

Keywords

Comments

Row 5 of A264550.

Examples

			Some solutions for n=4
..1..2..5..6..7....1..5..3..6..8....1..2..5..4..7....1..5..3..6..7
..0.10..8..3..4....0..7..2..9..4....0.10..8..3.12....0.10..2..9..4
.11.12.15.14..9...11.15.13.16.18...11..6.13.17..9...11.12.13..8.17
.16.17.18.13.22...10.17.12.19.14...16.20.21.22.14...16.20.18.19.14
.21.25.23.26.19...21.25.23.26.28...15.25.23.18.19...15.25.23.27.28
.20.27.28.29.24...20.27.22.29.24...26.27.28.29.24...26.21.22.29.24

Links

Crossrefs

Cf. A264550.
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