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.

A187858 Number of 3-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 2, 81, 254, 578, 1030, 1610, 2318, 3154, 4118, 5210, 6430, 7778, 9254, 10858, 12590, 14450, 16438, 18554, 20798, 23170, 25670, 28298, 31054, 33938, 36950, 40090, 43358, 46754, 50278, 53930, 57710, 61618, 65654, 69818, 74110, 78530, 83078, 87754, 92558
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 3 of A187857.

Examples

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

Links

Crossrefs

Cf. A187857.

Formula

Empirical: a(n) = 64*n^2 - 252*n + 238 for n>3.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: x^2*(2 + 75*x + 17*x^2 + 57*x^3 - 23*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A187859 Number of 4-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 216, 968, 2754, 5428, 9237, 14040, 19837, 26628, 34413, 43192, 52965, 63732, 75493, 88248, 101997, 116740, 132477, 149208, 166933, 185652, 205365, 226072, 247773, 270468, 294157, 318840, 344517, 371188, 398853, 427512, 457165, 487812
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 4 of A187857.

Examples

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

Links

Crossrefs

Cf. A187857.

Formula

Empirical: a(n) = 497*n^2 - 2652*n + 3448 for n>5.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: x^3*(216 + 320*x + 498*x^2 - 146*x^3 + 247*x^4 - 141*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187860 Number of 5-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 486, 3320, 11986, 26836, 50378, 81124, 120051, 166504, 220483, 281988, 351019, 427576, 511659, 603268, 702403, 809064, 923251, 1044964, 1174203, 1310968, 1455259, 1607076, 1766419, 1933288, 2107683, 2289604, 2479051, 2676024, 2880523
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 5 of A187857.

Examples

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

Links

Crossrefs

Cf. A187857.

Formula

Empirical: a(n) = 3763*n^2 - 25044*n + 40644 for n>7.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: x^3*(486 + 1862*x + 3484*x^2 + 352*x^3 + 2508*x^4 - 1488*x^5 + 977*x^6 - 655*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187861 Number of 6-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 846, 9932, 47962, 126397, 262409, 452766, 707541, 1017934, 1387600, 1813854, 2296696, 2836126, 3432144, 4084750, 4793944, 5559726, 6382096, 7261054, 8196600, 9188734, 10237456, 11342766, 12504664, 13723150, 14998224, 16329886, 17718136
Offset: 1

Views

Author

R. H. Hardin, Mar 14 2011

Keywords

Comments

Row 6 of A187857.

Examples

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

Links

Crossrefs

Cf. A187857.

Formula

Empirical: a(n) = 28294*n^2 - 224508*n + 433614 for n>9.
Conjectures from Colin Barker, Apr 26 2018: (Start)
G.f.: x^3*(846 + 7394*x + 20704*x^2 + 11461*x^3 + 17172*x^4 - 3232*x^5 + 10073*x^6 - 8800*x^7 + 3655*x^8 - 2685*x^9) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
(End)

A187862 Number of 7-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 1206, 26584, 180750, 568870, 1314428, 2456614, 4062007, 6094090, 8589253, 11504726, 14853686, 18625870, 22821278, 27439910, 32481766, 37946846, 43835150, 50146678, 56881430, 64039406, 71620606, 79625030, 88052678, 96903550
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 7 of A187857

Examples

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

Links

Formula

Empirical: a(n) = 211612*n^2 - 1941340*n + 4328678 for n>11

A187863 Number of 8-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 1008, 61668, 636102, 2432312, 6343874, 12918800, 22675997, 35694138, 52156394, 71825663, 94825088, 120967427, 150298947, 182782127, 218416967, 257203467, 299141627, 344231447, 392472927, 443866067, 498410867, 556107327
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 8 of A187857

Examples

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

Links

Formula

Empirical: a(n) = 1575830*n^2 - 16367550*n + 41250447 for n>13

A187864 Number of 9-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 414, 124880, 2090520, 9934272, 29607932, 65963326, 123580937, 204771252, 310971475, 441931786, 597915172, 777662238, 981570648, 1208872830, 1459728029, 1734003242, 2031698469, 2352813710, 2697348965, 3065304234, 3456679517
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 9 of A187857

Examples

			Some solutions for 4X4
..0..0..4..0....0..5..0..0....0..0..0..0....0..0..2..0....5..4..0..0
..9..0..6..3....0..4..3..7....0..5..7..6....4..0..1..8....0..3..2..1
..0..8..5..2....1..0..2..6....2..4..3..9....0..3..0..7....6..8..7..9
..0..0..7..1....0..0..9..8....1..8..0..0....0..6..5..9....0..0..0..0

Links

Formula

Empirical: a(n) = 11710007*n^2 - 135575032*n + 380311550 for n>15

A187865 Number of 10-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-queen's tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 219008, 6387404, 38766870, 133665550, 327612556, 658127610, 1150253908, 1821396586, 2678117739, 3721029612, 4946379865, 6353213493, 7935533922, 9694577705, 11627337878, 13734354068, 16015165378, 18469771808, 21098173358
Offset: 1

Views

Author

R. H. Hardin Mar 14 2011

Keywords

Comments

Row 10 of A187857

Examples

			Some solutions for 4X4
..0..9..0..0....9..8..3..2....0..9..8..5....0..0..6..0....0..1.10..2
..7..3..8..0....0..7..0..1....0..4..1..7....4..1..5..8....9..4..0..0
..0..6..2.10...10..4..6..5...10..3..0..6....3..7..0.10....0..8..3..0
..1..0..5..4....0..0..0..0....0..0..2..0....0..2..0..9....5..7..6..0

Links

Formula

Empirical: a(n) = 86897560*n^2 - 1108193530*n + 3420011978 for n>17
Showing 1-8 of 8 results.

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