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 1-7 of 7 results.

A187587 Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 5, 84, 286, 604, 1038, 1588, 2254, 3036, 3934, 4948, 6078, 7324, 8686, 10164, 11758, 13468, 15294, 17236, 19294, 21468, 23758, 26164, 28686, 31324, 34078, 36948, 39934, 43036, 46254, 49588, 53038, 56604, 60286, 64084, 67998, 72028, 76174, 80436, 84814
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Examples

			Some solutions for 4X4
..0..0..0..0....0..0..0..0....0..2..0..0....0..0..0..0....0..0..2..4
..0..0..1..0....0..0..0..0....1..3..0..0....0..0..0..0....0..1..3..0
..0..0..2..3....0..0..2..3....0..4..0..0....0..0..2..4....0..0..0..0
..0..0..0..4....0..1..0..4....0..0..0..0....0..1..3..0....0..0..0..0

Links

Crossrefs

Row 4 of A187586.

Formula

Empirical: a(n) = 58*n^2 - 204*n + 174 for n>2.
Empirical g.f.: x^2*(5+69*x+49*x^2-7*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

A187588 Number of 5-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 106, 578, 1484, 2794, 4508, 6626, 9148, 12074, 15404, 19138, 23276, 27818, 32764, 38114, 43868, 50026, 56588, 63554, 70924, 78698, 86876, 95458, 104444, 113834, 123628, 133826, 144428, 155434, 166844, 178658, 190876, 203498, 216524
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Comments

Row 5 of A187586.

Examples

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

Links

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 202*n^2 - 912*n + 994 for n>3.
Empirical G.f.: 2*x^3*(53+130*x+34*x^2-15*x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

A187589 Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 104, 1069, 3514, 7480, 12874, 19696, 27946, 37624, 48730, 61264, 75226, 90616, 107434, 125680, 145354, 166456, 188986, 212944, 238330, 265144, 293386, 323056, 354154, 386680, 420634, 456016, 492826, 531064, 570730, 611824, 654346, 698296
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Comments

Row 6 of A187586.

Examples

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

Links

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 714*n^2 - 3888*n + 5104 for n>4.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(104 + 757*x + 619*x^2 + 41*x^3 - 93*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A187590 Number of 7-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 78, 1708, 7666, 19104, 35832, 57592, 84384, 116208, 153064, 194952, 241872, 293824, 350808, 412824, 479872, 551952, 629064, 711208, 798384, 890592, 987832, 1090104, 1197408, 1309744, 1427112, 1549512, 1676944, 1809408, 1946904, 2089432
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Comments

Row 7 of A187586.

Examples

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

Links

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 2516*n^2 - 15980*n + 24408 for n>5.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: 2*x^3*(39 + 737*x + 1388*x^2 + 576*x^3 - 95*x^4 - 129*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187591 Number of 8-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 34, 2309, 15056, 45718, 95776, 164135, 250132, 353767, 475040, 613951, 770500, 944687, 1136512, 1345975, 1573076, 1817815, 2080192, 2360207, 2657860, 2973151, 3306080, 3656647, 4024852, 4410695, 4814176, 5235295, 5674052, 6130447, 6604480
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Comments

Row 8 of A187586.

Examples

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

Links

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 8819*n^2 - 63926*n + 111127 for n>6.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(34 + 2207*x + 8231*x^2 + 7443*x^3 + 1481*x^4 - 1095*x^5 - 663*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)

A187592 Number of 9-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 13, 2792, 27252, 103108, 246792, 458018, 732810, 1069534, 1468190, 1928778, 2451298, 3035750, 3682134, 4390450, 5160698, 5992878, 6886990, 7843034, 8861010, 9940918, 11082758, 12286530, 13552234, 14879870, 16269438, 17720938, 19234370
Offset: 1

Views

Author

R. H. Hardin, Mar 11 2011

Keywords

Comments

Row 9 of A187586.

Examples

			Some solutions for 4 X 4:
..0..0..7..8....3..0..0..9....0..0..8..9....6..8..9..0....0..4..0..0
..5..6..0..9....4..2..8..0....0..1..6..7....7..5..0..0....0..5..3..1
..2..4..0..0....5..7..1..0....0..2..4..5....4..2..0..0....8..6..0..2
..3..1..0..0....6..0..0..0....0..3..0..0....0..3..1..0....9..7..0..0

Links

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 30966*n^2 - 251630*n + 489234 for n>7.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(13 + 2753*x + 18915*x^2 + 29715*x^3 + 16432*x^4 - 286*x^5 - 3976*x^6 - 1634*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187593 Number of 10-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 3108, 45960, 219432, 609070, 1243461, 2111652, 3201436, 4508924, 6034116, 7777012, 9737612, 11915916, 14311924, 16925636, 19757052, 22806172, 26072996, 29557524, 33259756, 37179692, 41317332, 45672676, 50245724, 55036476, 60044932
Offset: 1

Views

Author

R. H. Hardin Mar 11 2011

Keywords

Comments

Row 10 of A187586

Examples

			Some solutions for 4X4
..0..8..9.10....0..7..8..9....0..0..0..2....0..8..9.10....0..0..0..0
..1..0..7..0....0..0..6.10....0..7..1..3....0..2..7..0....1..0..7..8
..2..0..5..6....2..3..4..5....0..8..6..4....0..3..1..6....2..6..0..9
..3..4..0..0....0..1..0..0....0..9.10..5....0..4..5..0....3..4..5.10

Formula

Empirical: a(n) = 108852*n^2 - 978404*n + 2100276 for n>8
Showing 1-7 of 7 results.

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