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 1-6 of 6 results.

A187173 Number of 3-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 16, 60, 128, 220, 336, 476, 640, 828, 1040, 1276, 1536, 1820, 2128, 2460, 2816, 3196, 3600, 4028, 4480, 4956, 5456, 5980, 6528, 7100, 7696, 8316, 8960, 9628, 10320, 11036, 11776, 12540, 13328, 14140, 14976, 15836, 16720, 17628, 18560, 19516, 20496
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 3 of A187172.

Examples

			Some solutions for 4 X 4:
..0..0..2..0....0..0..1..0....0..0..0..0....0..0..0..0....0..0..1..0
..3..0..0..0....0..0..0..0....3..0..0..0....0..0..2..0....2..0..0..0
..0..0..0..1....0..0..0..2....0..0..0..1....3..0..0..0....0..0..0..0
..0..0..0..0....0..3..0..0....0..2..0..0....0..0..0..1....0..3..0..0

Links

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 12*n^2 - 64*n + 80 for n>3.
G.f.: 4*x^4*(4 - x)*(1 + x) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

A187174 Number of 4-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 8, 48, 176, 384, 664, 1016, 1440, 1936, 2504, 3144, 3856, 4640, 5496, 6424, 7424, 8496, 9640, 10856, 12144, 13504, 14936, 16440, 18016, 19664, 21384, 23176, 25040, 26976, 28984, 31064, 33216, 35440, 37736, 40104, 42544, 45056, 47640, 50296
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

			Some solutions for 4 X 4:
..0..0..1..0....0..0..3..0....0..0..4..0....0..0..2..0....0..0..1..0
..4..0..0..0....4..0..0..0....3..0..0..0....1..0..0..0....2..0..0..0
..0..0..0..2....0..0..0..2....0..0..0..1....0..0..0..3....0..0..0..4
..0..3..0..0....0..1..0..0....0..2..0..0....0..4..0..0....0..3..0..0

Links

Crossrefs

Row 4 of A187172.

Formula

Empirical: a(n) = 36*n^2 - 260*n + 440 for n>5.
G.f.: 8*x^4*(1 + 3*x + 7*x^2 - x^3 - x^4) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

A187175 Number of 5-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 0, 16, 136, 456, 1024, 1804, 2784, 3964, 5344, 6924, 8704, 10684, 12864, 15244, 17824, 20604, 23584, 26764, 30144, 33724, 37504, 41484, 45664, 50044, 54624, 59404, 64384, 69564, 74944, 80524, 86304, 92284, 98464, 104844, 111424, 118204, 125184
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 5 of A187172.

Examples

			Some solutions for 5 X 5:
..1..0..0..0..0....0..0..3..0..0....0..0..0..0..1....0..0..0..0..5
..0..0..0..3..0....2..0..0..0..0....0..0..2..0..0....0..0..4..0..0
..0..2..0..0..0....0..0..0..4..0....3..0..0..0..0....1..0..0..0..0
..0..0..0..0..4....0..1..0..0..0....0..0..0..5..0....0..0..0..3..0
..0..0..5..0..0....0..0..0..0..5....0..4..0..0..0....0..2..0..0..0

Links

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 100*n^2 - 920*n + 1984 for n>7.
G.f.: 4*x^5*(2 - x)*(2 + 12*x + 18*x^2 + 15*x^3 + 3*x^4) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

A187176 Number of 6-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 0, 0, 88, 496, 1440, 3064, 5344, 8208, 11640, 15640, 20208, 25344, 31048, 37320, 44160, 51568, 59544, 68088, 77200, 86880, 97128, 107944, 119328, 131280, 143800, 156888, 170544, 184768, 199560, 214920, 230848, 247344, 264408, 282040
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 6 of A187172.

Examples

			Some solutions for 6 X 6:
..0..0..0..5..0..0....0..0..0..0..0..0....0..0..4..0..0..0....0..0..0..6..0..0
..0..6..0..0..0..0....0..0..0..0..6..0....3..0..0..0..0..0....0..1..0..0..0..0
..0..0..0..0..4..0....0..0..5..0..0..0....0..0..0..5..0..0....0..0..0..0..5..0
..0..0..1..0..0..0....4..0..0..0..0..1....0..2..0..0..0..0....0..0..2..0..0..0
..0..0..0..0..0..3....0..0..0..2..0..0....0..0..0..0..6..0....0..0..0..0..0..4
..0..0..0..2..0..0....0..3..0..0..0..0....0..0..1..0..0..0....0..0..0..3..0..0

Links

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 284*n^2 - 3100*n + 7944 for n>9.
G.f.: 8*x^6*(11 + 29*x + 27*x^2 + 18*x^3 - 3*x^4 - 9*x^5 - 2*x^6) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

A187177 Number of 7-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 0, 0, 16, 368, 1600, 4284, 8760, 15104, 23144, 32764, 43944, 56684, 70984, 86844, 104264, 123244, 143784, 165884, 189544, 214764, 241544, 269884, 299784, 331244, 364264, 398844, 434984, 472684, 511944, 552764, 595144, 639084, 684584
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 7 of A187172.

Examples

			Some solutions for 6 X 6:
..0..0..3..0..0..0....0..1..0..0..0..0....0..0..0..6..0..0....0..0..0..4..0..0
..4..0..0..0..0..1....0..0..0..0..7..0....0..7..0..0..0..0....0..5..0..0..0..0
..0..0..0..2..0..0....0..0..2..0..0..0....0..0..0..0..5..0....0..0..0..0..3..0
..0..5..0..0..0..0....3..0..0..0..0..6....0..0..2..0..0..0....0..0..6..0..0..0
..0..0..0..0..7..0....0..0..0..5..0..0....1..0..0..0..0..4....7..0..0..0..0..2
..0..0..6..0..0..0....0..4..0..0..0..0....0..0..0..3..0..0....0..0..0..1..0..0

Links

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 780*n^2 - 9880*n + 29384 for n>11.
G.f.: 4*x^6*(4 + 80*x + 136*x^2 + 143*x^3 + 85*x^4 + 19*x^5 - 43*x^6 - 29*x^7 - 5*x^8) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

A187178 Number of 8-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 280, 1784, 5944, 14072, 27104, 45288, 68400, 96048, 128064, 164424, 205128, 250176, 299568, 353304, 411384, 473808, 540576, 611688, 687144, 766944, 851088, 939576, 1032408, 1129584, 1231104, 1336968, 1447176, 1561728, 1680624
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 8 of A187172.

Examples

			Some solutions for 7 X 7:
..0..0..0..4..0..0..0....0..0..0..0..4..0..0....0..0..0..0..0..0..0
..0..5..0..0..0..0..0....0..0..3..0..0..0..0....0..0..0..0..8..0..0
..0..0..0..0..3..0..0....2..0..0..0..0..5..0....0..0..7..0..0..0..0
..0..0..6..0..0..0..0....0..0..0..8..0..0..0....6..0..0..0..0..1..0
..7..0..0..0..0..2..0....0..1..0..0..0..0..6....0..0..0..4..0..0..0
..0..0..0..1..0..0..0....0..0..0..0..7..0..0....0..5..0..0..0..0..2
..0..8..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..3..0..0

Links

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 2172*n^2 - 30972*n + 103944 for n>13.
Empirical g.f.: 8*x^7*(35 + 118*x + 179*x^2 + 164*x^3 + 117*x^4 + 31*x^5 - 28*x^6 - 49*x^7 - 21*x^8 - 3*x^9) / (1 - x)^3. - Colin Barker, Apr 22 2018
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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