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 1-8 of 8 results.

A187508 Number of 3-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 6, 31, 74, 135, 214, 311, 426, 559, 710, 879, 1066, 1271, 1494, 1735, 1994, 2271, 2566, 2879, 3210, 3559, 3926, 4311, 4714, 5135, 5574, 6031, 6506, 6999, 7510, 8039, 8586, 9151, 9734, 10335, 10954, 11591, 12246, 12919, 13610, 14319, 15046, 15791
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Examples

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

Links

Crossrefs

Row 3 of A187507.

Formula

Empirical: a(n) = 9*n^2 - 20*n + 10 for n>1.
Empirical g.f.: x^2*(6+13*x-x^2)/(1-x)^3. - Colin Barker, Jan 22 2012

A187509 Number of 4-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 2, 36, 115, 236, 399, 604, 851, 1140, 1471, 1844, 2259, 2716, 3215, 3756, 4339, 4964, 5631, 6340, 7091, 7884, 8719, 9596, 10515, 11476, 12479, 13524, 14611, 15740, 16911, 18124, 19379, 20676, 22015, 23396, 24819, 26284, 27791, 29340, 30931, 32564, 34239
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Examples

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

Links

Crossrefs

Row 4 of A187507.

Formula

Empirical: a(n) = 21*n^2 - 68*n + 51 for n>2.
Empirical g.f.: x^2*(2+30*x+13*x^2-3*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

A187510 Number of 5-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 40, 184, 435, 788, 1243, 1800, 2459, 3220, 4083, 5048, 6115, 7284, 8555, 9928, 11403, 12980, 14659, 16440, 18323, 20308, 22395, 24584, 26875, 29268, 31763, 34360, 37059, 39860, 42763, 45768, 48875, 52084, 55395, 58808, 62323, 65940, 69659, 73480
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Examples

			Some solutions for 4X4
..0..0..0..0....0..0..0..0....0..0..0..0....4..0..0..0....0..1..0..0
..0..0..0..0....0..0..0..0....4..5..0..0....5..3..1..0....0..2..0..0
..0..5..3..1....0..0..4..5....2..3..0..0....0..0..2..0....0..3..4..5
..0..0..4..2....0..1..2..3....0..1..0..0....0..0..0..0....0..0..0..0

Links

Crossrefs

Row 5 of A187507.

Formula

Empirical: a(n) = 51*n^2 - 208*n + 200 for n>3.
Empirical g.f.: x^3*(40+64*x+3*x^2-5*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

A187511 Number of 6-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 36, 272, 772, 1525, 2524, 3769, 5260, 6997, 8980, 11209, 13684, 16405, 19372, 22585, 26044, 29749, 33700, 37897, 42340, 47029, 51964, 57145, 62572, 68245, 74164, 80329, 86740, 93397, 100300, 107449, 114844, 122485, 130372, 138505, 146884
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Comments

Row 6 of A187507.

Examples

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

Links

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 123*n^2 - 600*n + 697 for n>4.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(36 + 164*x + 64*x^2 - 11*x^3 - 7*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 20, 330, 1224, 2726, 4807, 7458, 10679, 14470, 18831, 23762, 29263, 35334, 41975, 49186, 56967, 65318, 74239, 83730, 93791, 104422, 115623, 127394, 139735, 152646, 166127, 180178, 194799, 209990, 225751, 242082, 258983, 276454, 294495
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Comments

Row 7 of A187507.

Examples

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

Links

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 285*n^2 - 1624*n + 2210 for n>5.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(1 + x)*(20 + 250*x + 44*x^2 - 20*x^3 - 9*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 12, 390, 1910, 4880, 9250, 14969, 22026, 30421, 40154, 51225, 63634, 77381, 92466, 108889, 126650, 145749, 166186, 187961, 211074, 235525, 261314, 288441, 316906, 346709, 377850, 410329, 444146, 479301, 515794, 553625, 592794, 633301
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Comments

Row 8 of A187507.

Examples

			Some solutions for 4X4
..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0
..4..5..6..0....3..4..5..6....5..0..0..0....2..6..7..8....6..4..2..0
..0..3..1..0....0..2..0..7....6..4..2..0....3..4..5..0....7..8..3..1
..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....0..0..0..0

Links

Formula

Empirical: a(n) = 669*n^2 - 4316*n + 6681 for n>6.
Empirical g.f.: x^3*(12 + 354*x + 776*x^2 + 308*x^3 - 50*x^4 - 51*x^5 - 11*x^6) / (1 - x)^3. - Colin Barker, Nov 27 2017

A187514 Number of 9-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 6, 450, 2872, 8522, 17564, 29834, 45255, 63814, 85511, 110346, 138319, 169430, 203679, 241066, 281591, 325254, 372055, 421994, 475071, 531286, 590639, 653130, 718759, 787526, 859431, 934474, 1012655, 1093974, 1178431, 1266026, 1356759
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Comments

Row 9 of A187507.

Examples

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

Links

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 1569*n^2 - 11252*n + 19434 for n>7.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(6 + 432*x + 1540*x^2 + 1250*x^3 + 164*x^4 - 164*x^5 - 77*x^6 - 13*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187515 Number of 10-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 398, 3868, 13796, 31548, 56952, 89684, 129637, 176796, 231161, 292732, 361509, 437492, 520681, 611076, 708677, 813484, 925497, 1044716, 1171141, 1304772, 1445609, 1593652, 1748901, 1911356, 2081017, 2257884, 2441957, 2633236
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2011

Keywords

Comments

Row 10 of A187507.

Examples

			Some solutions for 4 X 4:
..1..0..0..0....7..8..9.10....0..7..8..9....0..5..0..1....0..0..0..1
..2..3..4..5....0..6..0..0....4..5..6.10....8..6..4..2....0..0..0..2
..0.10..8..6....0..4..5..0....0..3..1..0....9..7..0..3....9..7..5..3
..0..0..9..7....1..2..3..0....0..0..2..0...10..0..0..0...10..8..6..4

Links

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 3603*n^2 - 28504*n + 54377 for n>8.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^4*(398 + 2674*x + 3386*x^2 + 1366*x^3 - 172*x^4 - 324*x^5 - 107*x^6 - 15*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)
Showing 1-8 of 8 results.

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