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 1-9 of 9 results.

A187287 Number of 2-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 8, 36, 80, 140, 216, 308, 416, 540, 680, 836, 1008, 1196, 1400, 1620, 1856, 2108, 2376, 2660, 2960, 3276, 3608, 3956, 4320, 4700, 5096, 5508, 5936, 6380, 6840, 7316, 7808, 8316, 8840, 9380, 9936, 10508, 11096, 11700, 12320, 12956, 13608, 14276, 14960, 15660
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Examples

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

Links

Crossrefs

Row 2 of A187286.
Cf. A014107.

Programs

Formula

Empirical: a(n) = 8*n^2 - 12*n for n>1.
Empirical g.f.: 4*x^2*(2+3*x-x^2)/(1-x)^3. - Colin Barker, Jan 22 2012

A187288 Number of 3-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 8, 108, 328, 672, 1128, 1696, 2376, 3168, 4072, 5088, 6216, 7456, 8808, 10272, 11848, 13536, 15336, 17248, 19272, 21408, 23656, 26016, 28488, 31072, 33768, 36576, 39496, 42528, 45672, 48928, 52296, 55776, 59368, 63072, 66888, 70816, 74856, 79008
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 3 of A187286.

Examples

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

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 56*n^2 - 160*n + 72 for n>3.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^2*(2 + 21*x + 7*x^2 + 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)

A187289 Number of 4-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 8, 288, 1256, 3084, 5712, 9120, 13288, 18216, 23904, 30352, 37560, 45528, 54256, 63744, 73992, 85000, 96768, 109296, 122584, 136632, 151440, 167008, 183336, 200424, 218272, 236880, 256248, 276376, 297264, 318912, 341320, 364488, 388416
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 4 of A187286.

Examples

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

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 380*n^2 - 1532*n + 1224 for n>5.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^2*(2 + 66*x + 104*x^2 + 43*x^3 - 15*x^4 - 5*x^5 - 5*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187290 Number of 5-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 720, 4576, 13640, 28224, 48232, 73408, 103692, 139056, 179500, 225024, 275628, 331312, 392076, 457920, 528844, 604848, 685932, 772096, 863340, 959664, 1061068, 1167552, 1279116, 1395760, 1517484, 1644288, 1776172, 1913136, 2055180, 2202304
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 5 of A187286.

Examples

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

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 2540*n^2 - 12896*n + 14016 for n>7.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^3*(180 + 604*x + 518*x^2 + 78*x^3 - 24*x^4 - 64*x^5 - 15*x^6 - 7*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187291 Number of 6-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 1440, 15424, 57288, 134408, 248208, 397152, 580328, 797160, 1047532, 1331408, 1648788, 1999672, 2384060, 2801952, 3253348, 3738248, 4256652, 4808560, 5393972, 6012888, 6665308, 7351232, 8070660, 8823592, 9610028, 10429968, 11283412
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 6 of A187286.

Examples

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

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 16752*n^2 - 101420*n + 136160 for n>9.
Conjectures from Colin Barker, Apr 22 2018: (Start)
G.f.: 4*x^3*(360 + 2776*x + 3834*x^2 + 1844*x^3 + 356*x^4 - 384*x^5 - 228*x^6 - 144*x^7 - 29*x^8 - 9*x^9) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
(End)

A187292 Number of 7-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 2304, 47648, 228512, 616752, 1241936, 2102944, 3192912, 4505424, 6037932, 7789392, 9759616, 11948560, 14356224, 16982608, 19827712, 22891536, 26174080, 29675344, 33395328, 37334032, 41491456, 45867600, 50462464, 55276048, 60308352
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 7 of A187286.

Examples

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

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 109360*n^2 - 763776*n + 1206864 for n>11.
Conjectures from Colin Barker, Apr 23 2018: (Start)
G.f.: 4*x^3*(576 + 10184*x + 23120*x^2 + 17964*x^3 + 7392*x^4 - 280*x^5 - 1716*x^6 - 1604*x^7 - 637*x^8 - 261*x^9 - 47*x^10 - 11*x^11) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.
(End)

A187293 Number of 8-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 2664, 134944, 866888, 2732016, 6049424, 10906120, 17282088, 25129488, 34417440, 45129696, 57260948, 70809512, 85775112, 102157696, 119957264, 139173816, 159807352, 181857872, 205325376, 230209864, 256511336, 284229792
Offset: 1

Views

Author

R. H. Hardin Mar 08 2011

Keywords

Comments

Row 8 of A187286

Examples

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

Links

Formula

Empirical: a(n) = 708492*n^2 - 5580668*n + 10074432 for n>13

A187294 Number of 9-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 1512, 345120, 3123680, 11693984, 28716816, 55430032, 92058752, 138378368, 194130148, 259136336, 333313864, 416629232, 509072912, 610642384, 721337268, 841157504, 970103092, 1108174032, 1255370324, 1411691968, 1577138964
Offset: 1

Views

Author

R. H. Hardin, Mar 08 2011

Keywords

Comments

Row 9 of A187286.

Links

Crossrefs

Cf. A187286.

Formula

Empirical: a(n) = 4562676*n^2 - 39873424*n + 80572112 for n>15.

A187295 Number of 10-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 789696, 10664384, 48391584, 132995984, 276318288, 482853584, 752575536, 1083942480, 1475455440, 1926184124, 2435663832, 3003713808, 3630272848, 4315325376, 5058867816, 5860899668, 6721420864, 7640431404, 8617931288
Offset: 1

Views

Author

R. H. Hardin Mar 08 2011

Keywords

Comments

Row 10 of A187286

Links

Formula

Empirical: a(n) = 29244672*n^2 - 280021012*n + 623972304 for n>17
Showing 1-9 of 9 results.

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