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 1-7 of 7 results.

A187378 Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 4, 40, 132, 278, 478, 732, 1040, 1402, 1818, 2288, 2812, 3390, 4022, 4708, 5448, 6242, 7090, 7992, 8948, 9958, 11022, 12140, 13312, 14538, 15818, 17152, 18540, 19982, 21478, 23028, 24632, 26290, 28002, 29768, 31588, 33462, 35390, 37372, 39408, 41498, 43642
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Examples

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

Links

Crossrefs

Row 4 of A187377.

Formula

Empirical: a(n) = 27*n^2 - 97*n + 88 for n>2.
Empirical g.f.: 2*x^2*(2+14*x+12*x^2-x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

A187379 Number of 5-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 40, 188, 487, 924, 1499, 2212, 3063, 4052, 5179, 6444, 7847, 9388, 11067, 12884, 14839, 16932, 19163, 21532, 24039, 26684, 29467, 32388, 35447, 38644, 41979, 45452, 49063, 52812, 56699, 60724, 64887, 69188, 73627, 78204, 82919, 87772, 92763, 97892
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Examples

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

Links

Crossrefs

Row 5 of A187377.

Formula

Empirical: a(n) = 69*n^2 - 322*n + 372 for n>3.
Empirical g.f.: x^3*(40+68*x+43*x^2-13*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

A187380 Number of 6-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 24, 264, 832, 1810, 3154, 4864, 6940, 9382, 12190, 15364, 18904, 22810, 27082, 31720, 36724, 42094, 47830, 53932, 60400, 67234, 74434, 82000, 89932, 98230, 106894, 115924, 125320, 135082, 145210, 155704, 166564, 177790, 189382, 201340
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Examples

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

Links

Crossrefs

Row 6 of A187377.

Formula

Empirical: a(n) = 183*n^2 - 1035*n + 1432 for n>4.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: 2*x^3*(12 + 96*x + 56*x^2 + 41*x^3 - 22*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A187381 Number of 7-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 18, 324, 1418, 3448, 6581, 10688, 15769, 21824, 28853, 36856, 45833, 55784, 66709, 78608, 91481, 105328, 120149, 135944, 152713, 170456, 189173, 208864, 229529, 251168, 273781, 297368, 321929, 347464, 373973, 401456, 429913, 459344
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Comments

Row 7 of A187377.

Examples

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

Links

Crossrefs

Cf. A187377.

Formula

Empirical: a(n) = 487*n^2 - 3198*n + 5104 for n>5.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^3*(18 + 270*x + 500*x^2 + 148*x^3 + 167*x^4 - 129*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)

A187382 Number of 8-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 404, 2140, 6380, 13220, 22996, 35366, 50330, 67888, 88040, 110786, 136126, 164060, 194588, 227710, 263426, 301736, 342640, 386138, 432230, 480916, 532196, 586070, 642538, 701600, 763256, 827506, 894350, 963788, 1035820, 1110446
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Examples

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

Links

Crossrefs

Row 8 of A187377.

Formula

Empirical: a(n) = 1297*n^2 - 9679*n + 17420 for n>6.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: 2*x^4*(202 + 464*x + 586*x^2 + 48*x^3 + 168*x^4 - 171*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)

A187383 Number of 9-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 340, 3060, 10320, 24892, 46412, 75567, 111492, 154187, 203652, 259887, 322892, 392667, 469212, 552527, 642612, 739467, 843092, 953487, 1070652, 1194587, 1325292, 1462767, 1607012, 1758027, 1915812, 2080367, 2251692, 2429787, 2614652
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Comments

Row 9 of A187377.

Links

Crossrefs

Cf. A187377.

Formula

Empirical: a(n) = 3385*n^2 - 28390*n + 56892 for n>7.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: x^4*(340 + 2040*x + 2160*x^2 + 2772*x^3 - 364*x^4 + 687*x^5 - 865*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)

A187384 Number of 10-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 0, 280, 3792, 17052, 44464, 92628, 159328, 245946, 350386, 472648, 612732, 770638, 946366, 1139916, 1351288, 1580482, 1827498, 2092336, 2374996, 2675478, 2993782, 3329908, 3683856, 4055626, 4445218, 4852632, 5277868, 5720926, 6181806
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2011

Keywords

Comments

Row 10 of A187377.

Links

Crossrefs

Cf. A187377.

Formula

Empirical: a(n) = 8911*n^2 - 82691*n + 181756 for n>8.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: 2*x^4*(140 + 1476*x + 3258*x^2 + 2202*x^3 + 3300*x^4 - 1108*x^5 + 691*x^6 - 1048*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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