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 1-5 of 5 results.

A187029 Number of 4-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 24, 1344, 7056, 19568, 39348, 66360, 100380, 141408, 189444, 244488, 306540, 375600, 451668, 534744, 624828, 721920, 826020, 937128, 1055244, 1180368, 1312500, 1451640, 1597788, 1750944, 1911108, 2078280, 2252460, 2433648, 2621844
Offset: 1

Views

Author

R. H. Hardin, Mar 02 2011

Keywords

Comments

Row 4 of A187027.

Examples

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

Links

Crossrefs

Cf. A187027.

Formula

Empirical: a(n) = 3504*n^2 - 18540*n + 24444 for n>5.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^2*(6 + 318*x + 774*x^2 + 602*x^3 + 117*x^4 - 9*x^5 - 56*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187028 Number of 3-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 24, 296, 1008, 2232, 3936, 6120, 8784, 11928, 15552, 19656, 24240, 29304, 34848, 40872, 47376, 54360, 61824, 69768, 78192, 87096, 96480, 106344, 116688, 127512, 138816, 150600, 162864, 175608
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 3 of A187027

Examples

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

Formula

Empirical: a(n) = 240*n^2 - 936*n + 912 for n>3

A187030 Number of 5-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 5120, 45152, 161256, 376248, 696992, 1121176, 1647008, 2273384, 3000304, 3827768, 4755776, 5784328, 6913424, 8143064, 9473248, 10903976, 12435248
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 5 of A187027

Examples

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

Formula

Empirical: a(n) = 50272*n^2 - 328792*n + 534104 for n>7

A187031 Number of 6-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 15760, 263000, 1251720, 3443028, 7080688, 12213336, 18821144, 26872340, 36353568
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 6 of A187027

Examples

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

A187032 Number of 7-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 36816, 1384152, 9151912, 30203792, 69641344, 129718288
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 7 of A187027

Examples

			Some solutions for 4X4
..3..0..2..0....0..0..6..0....0..3..4..0....0..7..0..0....0..0..0..0
..0..7..0..1....0..2..0..7....2..5..6..0....6..0..5..4....0..2..0..0
..4..6..5..0....0..1..5..0....1..7..0..0....2..1..0..0....0..1..6..0
..0..0..0..0....0..4..0..3....0..0..0..0....0..3..0..0....4..3..5..7
Showing 1-5 of 5 results.

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