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.

A187851 Number of 3-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 24, 304, 1056, 2312, 4048, 6264, 8960, 12136, 15792, 19928, 24544, 29640, 35216, 41272, 47808, 54824, 62320, 70296, 78752, 87688, 97104, 107000, 117376, 128232, 139568, 151384, 163680, 176456, 189712, 203448, 217664, 232360, 247536, 263192
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 3 of A187850.

Examples

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

Links

Crossrefs

Cf. A187850.

Formula

Empirical: a(n) = 240*n^2 - 904*n + 832 for n>3.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 8*x^2*(3 + 29*x + 27*x^2 + 4*x^3 - 3*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A187852 Number of 4-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 24, 1400, 7620, 20952, 41652, 69456, 104268, 146088, 194916, 250752, 313596, 383448, 460308, 544176, 635052, 732936, 837828, 949728, 1068636, 1194552, 1327476, 1467408, 1614348, 1768296, 1929252, 2097216, 2272188, 2454168, 2643156
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 4 of A187850.

Examples

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

Links

Crossrefs

Cf. A187850.

Formula

Empirical: a(n) = 3504*n^2 - 17748*n + 21996 for n>5.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 4*x^2*(6 + 332*x + 873*x^2 + 567*x^3 + 64*x^4 - 66*x^5 - 24*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187853 Number of 5-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 5328, 49776, 177040, 408048, 744696, 1183632, 1723120, 2362864, 3102864, 3943120, 4883632, 5924400, 7065424, 8306704, 9648240, 11090032, 12632080, 14274384, 16016944, 17859760, 19802832, 21846160, 23989744, 26233584, 28577680
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 5 of A187850.

Examples

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

Links

Crossrefs

Cf. A187850.

Formula

Empirical: a(n) = 50128*n^2 - 312688*n + 476944 for n>7.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 8*x^3*(666 + 4224*x + 5462*x^2 + 2616*x^3 + 237*x^4 - 419*x^5 - 217*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)

A187854 Number of 6-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 16032, 292776, 1400168, 3807828, 7700944, 13082348, 19910456, 28160124, 37824352, 48902340, 61394088, 75299596, 90618864, 107351892, 125498680, 145059228, 166033536, 188421604, 212223432, 237439020, 264068368, 292111476
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 6 of A187850.

Examples

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

Links

Crossrefs

Cf. A187850.

Formula

Empirical: a(n) = 706880*n^2 - 5180252*n + 9274644 for n>9.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: 4*x^3*(4008 + 61170*x + 142484*x^2 + 117405*x^3 + 46297*x^4 + 708*x^5 - 10396*x^6 - 6286*x^7 - 1750*x^8 - 200*x^9) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
(End)

A187855 Number of 7-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 35328, 1533064, 10353632, 33908456, 76860784, 140714528, 225295032, 330074144, 454720992, 599118736, 763244128, 947095136, 1150671760, 1373974000, 1617001856, 1879755328, 2162234416, 2464439120, 2786369440, 3128025376
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 7 of A187850

Examples

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

Links

Formula

Empirical: a(n) = 9862808*n^2 - 82444808*n + 168212080 for n>11

A187856 Number of 8-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 49536, 7067600, 71450504, 288493336, 741624088, 1474319716, 2497432760, 3806665836, 5395343360, 7259273932, 9396774760, 11807403172, 14491089616, 17447829164, 20677621816, 24180467572, 27956366432, 32005318396, 36327323464
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 8 of A187850

Examples

			Some solutions for 3X3
..8..5..2....0..8..4....5..4..3....8..4..6....0..4..7....8..4..5....8..4..1
..7..6..1....3..7..1....8..2..6....5..3..7....5..2..8....2..0..7....7..2..3
..4..3..0....6..5..2....0..1..7....0..1..2....1..6..3....1..6..3....5..6..0

Links

Formula

Empirical: a(n) = 136526552*n^2 - 1275583564*n + 2906368876 for n>13
Showing 1-6 of 6 results.

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