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

A264670 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 2, 9, 19, 44, 108, 264, 649, 1573, 3837, 9353, 22801, 55571, 135432, 330113, 804604, 1961113, 4779902, 11650318, 28396001, 69211142, 168692149, 411162676, 1002149647, 2442594935, 5953472042, 14510727488, 35367800720, 86203902041
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Examples

			Some solutions for n=4:
..5..0..1....4..0..1....5..0..1....4..0..1....4..0..1....5..0..1....8..0..1
.11..3..2...11..8..2....8..3..2....8..3..2....7..8..2...11..8..2...11..3..2
.10..4..7....3..6..5...11..4..7...14.11..5....3..6..5....3..4..7...14..4..5
..6.14..8...14..7.10....6.14.10....6..7.10...13.14.10....6.14.10....6..7.10
..9.12.13....9.12.13....9.12.13....9.12.13....9.12.11....9.12.13....9.12.13

Links

Crossrefs

Column 2 of A264676.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3) + 3*a(n-4) + 2*a(n-5) - a(n-6) + 4*a(n-7) - a(n-8) - a(n-10).
Empirical g.f.: x*(1 + 5*x^2 + x^4 + 3*x^5 - x^6 - x^8) / (1 - 2*x - x^3 - 3*x^4 - 2*x^5 + x^6 - 4*x^7 + x^8 + x^10). - Colin Barker, Jan 08 2019

A264671 Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 10, 34, 145, 603, 2417, 9976, 40825, 166985, 684253, 2801318, 11470702, 46972259, 192337615, 787587465, 3225016272, 13205769817, 54075000313, 221426203265, 906695582830, 3712735776142, 15202904012125, 62252826121583
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Column 3 of A264676.

Examples

			Some solutions for n=4
..6..7..1..2....6..0..1..2....5..0..1..2....5..0..1..2....6..0..1..2
..0..4..5..3...10..4..5..3...10..4.11..3....9..4.11..3...14.10..5..3
.13..8.15.10...13.14.15..7...13.15..6..7...13.15..6..7....4.15..9..7
.17..9.19.11....8..9.19.11....8..9.19.14....8.19.10.14....8.19.13.11
.12.16.14.18...12.16.17.18...12.16.17.18...12.16.17.18...12.16.17.18

Links

Crossrefs

Cf. A264676.

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) +10*a(n-3) +6*a(n-5) +11*a(n-6) +4*a(n-7) +22*a(n-8) +21*a(n-9) -4*a(n-10) -10*a(n-11) -10*a(n-12) -2*a(n-13) +a(n-15)

A264672 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 29, 123, 890, 6851, 43131, 291315, 1980287, 13199209, 88670692, 595721002, 3995710025, 26820625288, 180019819900, 1208161823995, 8108780202591, 54422802858380, 365262503014440, 2451492555516290, 16453389631984472
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Column 4 of A264676.

Examples

			Some solutions for n=4
.12..0..1..9..3....7..0..9..2..3....6..0..1..9..3...12..0..1..2..3
.11..5..2..7..4...12..1..6.14..4...12..5..2..7..4...17.18..6..7..4
.17..6.19..8.13....5.17.19..8.13...16.18.24..8.13....5.23.24..8..9
.10.22.16.24.14...10.11.16.24.18...10.11.23.17.14...10.11.16.13.14
.15.20.21.18.23...15.20.21.22.23...15.20.21.22.19...15.20.21.22.19

Links

Crossrefs

Cf. A264676.

Formula

Empirical: a(n) = 3*a(n-1) +9*a(n-2) +106*a(n-3) +212*a(n-5) -1161*a(n-6) +560*a(n-7) -3942*a(n-8) -6220*a(n-9) +2684*a(n-10) -18488*a(n-11) +10184*a(n-12) +76448*a(n-13) +97808*a(n-14) +177984*a(n-15) +21920*a(n-16) +647104*a(n-17) +834688*a(n-18) +224000*a(n-19) +513280*a(n-20) -413184*a(n-21) +221952*a(n-22) -379392*a(n-23) +216576*a(n-24) +258048*a(n-25) -73728*a(n-26) for n>27.

A264673 Number of (n+1)X(5+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 75, 748, 9205, 123222, 1449467, 17406354, 209749118, 2503676777, 29934965340, 358006964177, 4278035445236, 51129215370129, 611086118399334, 7303034816210073, 87279407453579353, 1043087592653373745
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Column 5 of A264676.

Examples

			Some solutions for n=4
..7..8..1..2..3..4....7..0..1..2..3..4...14..0..1.10..3..4....7..0.16.10..3..4
..0..6.16.23.17..5...14..6.16..8..9..5...20.15..2.16.17..5...13..1..2.23..9..5
.19.20.13..9.10.11...26.12.13.23.10.11....6..7..8..9.23.11....6.27..8.14.15.11
.12.26.14.15.29.22...25.27.19.15.29.17...12.13.19.29.21.22...12.26.19.20.29.17
.18.24.25.21.27.28...18.24.20.21.22.28...18.24.25.26.27.28...18.24.25.21.22.28

Links

Crossrefs

Cf. A264676.

A264674 Number of (n+1)X(6+1) arrays of permutations of 0..n*7+6 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

3, 201, 3698, 88687, 2025372, 43095017, 918298857, 19297801298, 404856272120, 8489260394876, 177705197746797, 3719732870934290, 77850133987381370, 1629084572098790038, 34089792233147972596, 713335964676746507000
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Column 6 of A264676.

Examples

			Some solutions for n=4
..8..9..1..2.13..4..5....8.17..1.12..3..4..5....9..0..1..2.13..4..5
..0.16.25..3.10.11..6....0..7..2..9.19.20..6...16.17..8..3.10.11..6
..7.23.24.26.17.12.19...22.14.24.10.11.18.13....7.31.24.26.27.12.19
.14.15.22.33.18.34.20...29.15.16.33.34.25.26...14.15.22.23.18.34.20
.21.28.29.30.31.32.27...21.28.23.30.31.32.27...21.28.29.30.25.32.33

Links

Crossrefs

Cf. A264676.

A264675 Number of (n+1)X(7+1) arrays of permutations of 0..n*8+7 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

3, 588, 17443, 714235, 29875350, 1095840260, 40765995197, 1494347569074, 54204721906375, 1966753578705875, 71178721732614714, 2573134003964620565, 93001271214814999684, 3360101883867911885437, 121381797022850227205242
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Column 7 of A264676.

Examples

			Some solutions for n=3
.18..0.12..2..3.14..5..6...10..0..1.13..3..4..5..6...10..0.12..2..3..4..5..6
.17..1..9.10..4.22.13..7...17.18..2.21.22.12.23..7...26..1.20.21.11.23.13..7
..8.27.28.11.19.30.31.15....8..9.27.11.19.31.14.15....8..9.17.18.29.31.14.15
.16.24.25.26.20.21.29.23...16.24.25.26.20.28.29.30...16.24.25.19.27.28.22.30

Links

Crossrefs

Cf. A264676.

A264677 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 2, 10, 29, 75, 201, 588, 1700, 4785, 13401, 37905, 107598, 304638, 860789, 2433555, 6885713, 19483112, 55110392, 155875521, 440924465, 1247301569, 3528321578, 9980556450, 28232081677, 79861067099, 225905953689, 639026458132
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Examples

			Some solutions for n=4:
.12..7..9..2..3....6..7..1..2..3....6.13..8..2..3...12..0..1..2..3
..0..1..6.14..4....0.12.13.14..4....0..1.14..7..4...11.13..6.14..4
..5.10.11..8.13....5.10.11..8..9....5.10.11.12..9....5.10..7..8..9

Links

Crossrefs

Row 2 of A264676.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 5*a(n-3) + 7*a(n-4) - 5*a(n-5) + 7*a(n-6) - 3*a(n-7) + a(n-8) - a(n-9).
Empirical g.f.: x*(1 - x + 7*x^2 + x^4 + 4*x^5 - 2*x^6 - x^8) / (1 - 3*x + 3*x^2 - 5*x^3 - 7*x^4 + 5*x^5 - 7*x^6 + 3*x^7 - x^8 + x^9). - Colin Barker, Jan 08 2019

A264678 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

0, 9, 34, 123, 748, 3698, 17443, 84737, 414665, 2005125, 9713004, 47127519, 228570355, 1108064547, 5372882058, 26053821399, 126333862510, 612577288197, 2970352085648, 14403091243503, 69839730071000, 338648374694336
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Row 3 of A264676.

Examples

			Some solutions for n=4
..7.13..1..2..3....6..0..1..2..3....7..8..1..2..3....6..0..8..2..3
..0.12.19.14..4...11..5.14..7..4....0..5..6.14..4...17..1.19..7..4
..5..6.11..8..9...16.17.19..8..9...16.17.11.19..9....5.18.11.12..9
.10.15.16.17.18...10.15.12.13.18...10.15.12.13.18...10.15.16.13.14

Links

Crossrefs

Cf. A264676.

Formula

Empirical: a(n) = 3*a(n-1) +7*a(n-2) +8*a(n-3) +63*a(n-4) -204*a(n-5) -330*a(n-6) -33*a(n-7) -753*a(n-8) +5131*a(n-9) +4454*a(n-10) -4248*a(n-11) +7015*a(n-12) -48191*a(n-13) -32905*a(n-14) +65323*a(n-15) -27694*a(n-16) +173763*a(n-17) +127266*a(n-18) -326578*a(n-19) +76681*a(n-20) -257552*a(n-21) -335862*a(n-22) +809888*a(n-23) -210179*a(n-24) +339020*a(n-25) +653025*a(n-26) -1539461*a(n-27) +207596*a(n-28) -364624*a(n-29) -1269055*a(n-30) +2691400*a(n-31) +488565*a(n-32) -214595*a(n-33) +1192214*a(n-34) -2335990*a(n-35) -1227030*a(n-36) +669413*a(n-37) -963255*a(n-38) +517564*a(n-39) +1507133*a(n-40) +62100*a(n-41) -84052*a(n-42) +492955*a(n-43) -482847*a(n-44) -398776*a(n-45) +148989*a(n-46) -138160*a(n-47) -38858*a(n-48) +119696*a(n-49) -8295*a(n-50) -25006*a(n-51) +22162*a(n-52) +4175*a(n-53) -10174*a(n-54) +6735*a(n-55) +1215*a(n-56) -3575*a(n-57) +1051*a(n-58) +12*a(n-59) -430*a(n-60) +67*a(n-61) +51*a(n-62) +27*a(n-63) -10*a(n-64) +8*a(n-65) +19*a(n-66) -8*a(n-67) -a(n-68) +3*a(n-69) -a(n-70)

A264679 Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

0, 19, 145, 890, 9205, 88687, 714235, 5871821, 50048019, 422792433, 3525222983, 29504247476, 247603962409, 2074917109436, 17373094676114, 145530813422748, 1219291683848838, 10213817024920997, 85555541651802803, 716687147462600097
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Row 4 of A264676.

Examples

			Some solutions for n=4
..6..0..1..2..3...12..0..1..9..3....6..0..1..2..3....6..0..1..2..3
.17.12.13..7..4...11.18..2..7..4...12..5.19..7..4...17.12.14..7..4
..5.18.11..8..9....5..6.24..8.13...16.10.11..8..9....5.23.24..8..9
.10.23.16.24.14...10.23.16.17.14...21.22.24.13.14...10.11.16.13.18
.15.20.21.22.19...15.20.21.22.19...15.20.17.18.23...15.20.21.22.19

Links

Crossrefs

Cf. A264676.

Formula

Empirical recurrence of order 81 (see link above)

A264680 Number of (5+1)X(n+1) arrays of permutations of 0..n*6+5 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

Original entry on oeis.org

1, 44, 603, 6851, 123222, 2025372, 29875350, 436294812, 6478725972, 95858657256, 1406076314579, 20604755924271, 302274882992297, 4432087245361391, 64934929110247763, 951285313173076076, 13937110096540031221
Offset: 1

Views

Author

R. H. Hardin, Nov 20 2015

Keywords

Comments

Row 5 of A264676.

Examples

			Some solutions for n=4
..6.13..1..2..3....7..8..1..2..3...12..8..1..9..3....6..0..1..9..3
..0.12.19..7..4....0..5..6.14..4....0..5..2..7..4...11..5..2.14..4
..5.18.11..8..9...17.10.11.12..9...16..6.11.19.13...17.10..7..8.13
.10.15.24.17.14...21.15.24.13.18...10.22.29.17.14...27.22.12.24.18
.26.16.21.29.23...27.16.29.22.19...15.28.21.18.23...15.16.21.29.19
.20.25.22.27.28...20.25.26.23.28...20.25.26.27.24...20.25.26.23.28

Links

Crossrefs

Cf. A264676.
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