A186857 Number of 8-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

16, 2208, 57392, 405040, 1508784, 3846192, 7777808, 13502064, 21089312, 30521216, 41748432, 54726992, 69434272, 85865344, 104020208, 123898864, 145501312, 168827552, 193877584, 220651408, 249149024, 279370432, 311315632, 344984624, 380377408, 417493984

Offset

1,1

Links

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

Formula

a(n) = 861896*n^2 - 6840120*n + 12695408 for n >= 12. - Andrew Howroyd, Jan 02 2023

Example

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

Prog

(PARI) row(8, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 02 2023

Crossrefs

Row 8 of A186851.

Sequence in context: A265593 A345275 A304399 * A196884 A165126 A241368

Adjacent sequences: A186854 A186855 A186856 * A186858 A186859 A186860

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Extensions

Terms a(8) and beyond from Andrew Howroyd, Jan 02 2023

Status

approved