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.

A187156 Number of 3-step one 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, 20, 64, 132, 224, 340, 480, 644, 832, 1044, 1280, 1540, 1824, 2132, 2464, 2820, 3200, 3604, 4032, 4484, 4960, 5460, 5984, 6532, 7104, 7700, 8320, 8964, 9632, 10324, 11040, 11780, 12544, 13332, 14144, 14980, 15840, 16724, 17632, 18564, 19520, 20500
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 3 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 12*n^2 - 40*n + 32 for n>1.
Conjectures from Colin Barker, Feb 28 2018: (Start)
G.f.: 4*x^3*(5 + x) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)

A187157 Number of 4-step one 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, 92, 248, 476, 776, 1148, 1592, 2108, 2696, 3356, 4088, 4892, 5768, 6716, 7736, 8828, 9992, 11228, 12536, 13916, 15368, 16892, 18488, 20156, 21896, 23708, 25592, 27548, 29576, 31676, 33848, 36092, 38408, 40796, 43256, 45788, 48392, 51068, 53816
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 4 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 36*n^2 - 168*n + 188 for n>2.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^3*(2 + 17*x - x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
(End)

A187158 Number of 5-step one 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, 72, 388, 904, 1620, 2536, 3652, 4968, 6484, 8200, 10116, 12232, 14548, 17064, 19780, 22696, 25812, 29128, 32644, 36360, 40276, 44392, 48708, 53224, 57940, 62856, 67972, 73288, 78804, 84520, 90436, 96552, 102868, 109384, 116100, 123016, 130132
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 5 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 100*n^2 - 584*n + 808 for n>3.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^4*(18 + 43*x - 11*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A187159 Number of 6-step one 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, 56, 456, 1588, 3288, 5556, 8392, 11796, 15768, 20308, 25416, 31092, 37336, 44148, 51528, 59476, 67992, 77076, 86728, 96948, 107736, 119092, 131016, 143508, 156568, 170196, 184392, 199156, 214488, 230388, 246856, 263892, 281496, 299668
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 6 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 284*n^2 - 1992*n + 3316 for n>4.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^4*(14 + 72*x + 97*x^2 - 41*x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A187160 Number of 7-step one 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, 16, 544, 2328, 6172, 11576, 18540, 27064, 37148, 48792, 61996, 76760, 93084, 110968, 130412, 151416, 173980, 198104, 223788, 251032, 279836, 310200, 342124, 375608, 410652, 447256, 485420, 525144, 566428, 609272, 653676, 699640, 747164
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 7 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 780*n^2 - 6296*n + 12024 for n>5.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^4*(4 + 124*x + 186*x^2 + 201*x^3 - 125*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187161 Number of 8-step one 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, 0, 472, 3504, 10576, 23340, 40448, 61900, 87696, 117836, 152320, 191148, 234320, 281836, 333696, 389900, 450448, 515340, 584576, 658156, 736080, 818348, 904960, 995916, 1091216, 1190860, 1294848, 1403180, 1515856, 1632876, 1754240
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Comments

Row 8 of A187155.

Examples

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

Links

Crossrefs

Cf. A187155.

Formula

Empirical: a(n) = 2172*n^2 - 19816*n + 42860 for n>6.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^5*(118 + 522*x + 370*x^2 + 413*x^3 - 337*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)
Showing 1-6 of 6 results.

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