A186866 - OEIS

A186866

Number of 7-step king's tours on an n X n board summed over all starting positions.

0, 0, 2984, 68272, 296360, 722384, 1335984, 2129440, 3102752, 4255920, 5588944, 7101824, 8794560, 10667152, 12719600, 14951904, 17364064, 19956080, 22727952, 25679680, 28811264, 32122704, 35614000, 39285152, 43136160, 47167024

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

From J. Volkmar Schmidt, Oct 24 2023 (Start)

Proof of a(n) follows proof scheme from David A. Corneth for A186864.

Distribution matrix of surrounding rectangles for 7-step walks is:

[0 0 0 0 0 0 2]

[0 0 0 800 1600 1024 252]

[0 0 2984 9780 7904 3360 644]

[0 800 9780 12416 6636 2272 388]

[0 1600 7904 6636 2912 864 136]

[0 1024 3360 2272 864 224 32]

[2 252 644 388 136 32 4]

(End)

LINKS

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

FORMULA

Empirical: a(n) = 89928*n^2 - 555464*n + 817760 for n>5.

EXAMPLE

Some solutions for 3X3

..0..2..1....0..2..0....6..0..0....1..7..6....1..2..3....7..2..1....6..5..0

..4..3..0....3..7..1....7..5..2....2..0..5....0..4..7....3..6..0....7..4..1

..5..6..7....4..5..6....4..3..1....3..4..0....0..6..5....5..4..0....0..2..3

CROSSREFS

Row 7 of A186861.

Sequence in context: A235503 A120373 A365258 * A252571 A231628 A231623

Adjacent sequences: A186863 A186864 A186865 * A186867 A186868 A186869

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2011

STATUS

approved

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.