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

Author

R. H. Hardin, Feb 27 2011

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 8 of A186851.

Programs

PARI

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

Formula

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

Extensions

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