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.

A187049 Number of 5-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 8, 456, 2896, 9216, 20648, 37472, 59524, 86656, 118868, 156160, 198532, 245984, 298516, 356128, 418820, 486592, 559444, 637376, 720388, 808480, 901652, 999904, 1103236, 1211648, 1325140, 1443712, 1567364, 1696096, 1829908, 1968800, 2112772
Offset: 1

Views

Author

R. H. Hardin, Mar 02 2011

Keywords

Comments

Row 5 of A187046.

Examples

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

Links

Crossrefs

Cf. A187046.

Formula

Empirical: a(n) = 2540*n^2 - 21128*n + 43936 for n>7.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^3*(2 + 108*x + 388*x^2 + 472*x^3 + 308*x^4 + 70*x^5 - 41*x^6 - 37*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187050 Number of 6-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 584, 6952, 29500, 79088, 162320, 281320, 435436, 623508, 845084, 1100164, 1388748, 1710836, 2066428, 2455524, 2878124, 3334228, 3823836, 4346948, 4903564, 5493684, 6117308, 6774436, 7465068, 8189204, 8946844, 9737988, 10562636
Offset: 1

Views

Author

R. H. Hardin, Mar 02 2011

Keywords

Comments

Row 6 of A187046.

Examples

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

Links

Crossrefs

Cf. A187046.

Formula

Empirical: a(n) = 16752*n^2 - 163720*n + 397436 for n>9.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^3*(146 + 1300*x + 2599*x^2 + 2715*x^3 + 1651*x^4 + 531*x^5 - 163*x^6 - 290*x^7 - 113*x^8) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
(End)

A187051 Number of 7-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 400, 14024, 86608, 285048, 668176, 1272720, 2110944, 3180724, 4475176, 5989600, 7722744, 9674608, 11845192, 14234496, 16842520, 19669264, 22714728, 25978912, 29461816, 33163440, 37083784, 41222848, 45580632, 50157136, 54952360
Offset: 1

Views

Author

R. H. Hardin, Mar 02 2011

Keywords

Comments

Row 7 of A187046.

Examples

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

Links

Crossrefs

Cf. A187046.

Formula

Empirical: a(n) = 109360*n^2 - 1219576*n + 3362248 for n>11.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^4*(100 + 3206*x + 11434*x^2 + 16724*x^3 + 14708*x^4 + 9182*x^5 + 3066*x^6 - 531*x^7 - 1721*x^8 - 1175*x^9 - 313*x^10) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.
(End)

A187052 Number of 8-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 80, 22200, 226864, 961728, 2625640, 5543744, 9907248, 15787528, 23174472, 32030516, 42322492, 54034656, 67163804, 81709936, 97673052, 115053152, 133850236, 154064304, 175695356, 198743392, 223208412, 249090416, 276389404, 305105376, 335238332, 366788272
Offset: 1

Views

Author

R. H. Hardin, Mar 02 2011

Keywords

Examples

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

Links

Crossrefs

Row 8 of A187046.

Formula

Empirical: a(n) = 708492*n^2 - 8834104*n + 27135516 for n>13.

A187047 Number of 3-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 28, 136, 360, 696, 1144, 1704, 2376, 3160, 4056, 5064, 6184, 7416, 8760, 10216, 11784, 13464, 15256, 17160, 19176, 21304, 23544, 25896, 28360, 30936, 33624, 36424, 39336, 42360, 45496, 48744, 52104, 55576, 59160
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 3 of A187046

Examples

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

Formula

Empirical: a(n) = 56*n^2 - 280*n + 360 for n>3

A187048 Number of 4-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 24, 272, 1084, 2660, 5032, 8164, 12056, 16708, 22120, 28292, 35224, 42916, 51368, 60580, 70552, 81284, 92776, 105028, 118040, 131812, 146344, 161636, 177688, 194500, 212072, 230404, 249496, 269348, 289960, 311332, 333464, 356356, 380008
Offset: 1

Views

Author

R. H. Hardin Mar 02 2011

Keywords

Comments

Row 4 of A187046

Examples

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

Formula

Empirical: a(n) = 380*n^2 - 2568*n + 4388 for n>5
Showing 1-6 of 6 results.

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