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.

A187191 Number of 4-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 8, 288, 2208, 9200, 27720, 68208, 146048, 282528, 505800, 851840, 1365408, 2101008, 3123848, 4510800, 6351360, 8748608, 11820168, 15699168, 20535200, 26495280, 33764808, 42548528, 53071488, 65580000, 80342600, 97651008
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

			Some solutions for 3X3
..0..4..0....2..1..0....0..1..2....1..0..0....0..0..4....4..2..3....3..2..0
..2..3..1....3..0..0....4..0..3....2..3..4....0..1..2....0..0..0....0..0..0
..0..0..0....4..0..0....0..0..0....0..0..0....0..0..3....0..1..0....4..1..0

Links

Crossrefs

Row 4 of A187189.

Formula

Empirical: a(n) = 8*n^5 - 34*n^4 + 48*n^3 - 22*n^2.
Empirical g.f.: 8*x^2*(1+30*x+75*x^2+14*x^3)/(1-x)^6. - Colin Barker, Jan 22 2012

A187190 Number of 3-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 8, 108, 480, 1400, 3240, 6468, 11648, 19440, 30600, 45980, 66528, 93288, 127400, 170100, 222720, 286688, 363528, 454860, 562400, 687960, 833448, 1000868, 1192320, 1410000, 1656200, 1933308, 2243808, 2590280, 2975400
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

			Some solutions for 3X3
..0..0..3....0..2..3....1..0..2....0..0..3....0..3..0....0..0..0....3..2..0
..0..1..2....0..1..0....0..0..0....0..0..2....0..2..1....0..2..3....0..0..0
..0..0..0....0..0..0....0..0..3....0..0..1....0..0..0....0..1..0....0..1..0

Crossrefs

Row 3 of A187189.

Formula

Empirical: a(n) = 4*n^4 - 10*n^3 + 6*n^2.
Empirical G.f.: 4*x^2*(2+17*x+5*x^2)/(1-x)^5. - Colin Barker, Jan 22 2012

A187192 Number of 5-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 720, 9792, 58800, 231840, 705600, 1800960, 4046112, 8251200, 15594480, 27720000, 46846800, 75889632, 118591200, 179665920, 264955200, 381594240, 538190352
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

			Some solutions for 3X3
..0..5..1....0..0..4....0..1..5....1..0..2....1..0..0....4..0..5....2..3..1
..0..0..2....2..0..3....0..3..4....0..5..0....2..0..5....3..0..0....0..0..0
..0..4..3....1..0..5....0..2..0....0..4..3....3..0..4....2..1..0....5..4..0

Crossrefs

Row 5 of A187189.

Formula

Empirical: a(n) = 16*n^6 - 98*n^5 + 228*n^4 - 238*n^3 + 92*n^2.
Empirical G.f.: 48*x^3*(15+99*x+112*x^2+14*x^3)/(1-x)^7. [Colin Barker, Jan 22 2012]

A187193 Number of 6-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 1440, 40896, 364800, 1902240, 7197120, 21960960, 57407616, 133531200, 283488480, 559247040, 1038660480
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

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

Crossrefs

Row 6 of A187189.

Formula

Empirical: a(n) = 32*n^7 - 258*n^6 + 846*n^5 - 1426*n^4 + 1234*n^3 - 428*n^2.
Empirical G.f.: 96*x^3*(15+306*x+812*x^2+503*x^3+44*x^4)/(1-x)^8. [Colin Barker, Jan 22 2012]

A187194 Number of 7-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 2304, 156672, 2169600, 15220800, 72182880, 264520704, 806827392, 2144534400, 5120913600, 11222069760
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

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

Crossrefs

Row 7 of A187189.

Formula

Empirical G.f.: -96*x^3*(287*x^5+4491*x^4+11886*x^3+8776*x^2+1416*x+24)/(x-1)^9. [Colin Barker, Jul 01 2012]

A187195 Number of 8-turn rook's tours on an n X n board summed over all starting positions.

Original entry on oeis.org

0, 0, 2664, 551232, 12319200, 118332000, 709921800, 3141298944, 11217854592, 34149988800, 91867386600, 223898241600
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2011

Keywords

Examples

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

Crossrefs

Row 8 of A187189.

Formula

Empirical: a(n) = 128*n^9 - 1538*n^8 + 7956*n^7 - 23556*n^6 + 44586*n^5 - 55218*n^4 + 40894*n^3 - 13252*n^2.
Empirical G.f.: 72*x^3 * (2599*x^6 +52838*x^5 +213575*x^4 +272580*x^3 +96205*x^2 +7286*x +37) / (x-1)^10. [Colin Barker, Jul 01 2012]
Showing 1-6 of 6 results.

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