A186856 Number of 7-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

16, 1280, 21664, 118480, 372384, 847520, 1584576, 2596480, 3879696, 5424848, 7224912, 9277856, 11583680, 14142384, 16953968, 20018432, 23335776, 26906000, 30729104, 34805088, 39133952, 43715696, 48550320, 53637824, 58978208, 64571472

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Formula

a(n) = 126440*n^2 - 855176*n + 1332608 for n >= 10. - Andrew Howroyd, Jan 02 2023

Example

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

Prog

(PARI) row(7, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 02 2023

Crossrefs

Row 7 of A186851.

Sequence in context: A222888 A113104 A227602 * A000490 A308587 A363921

Adjacent sequences: A186853 A186854 A186855 * A186857 A186858 A186859

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 02 2023

Status

approved