A186853 Number of 4-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

16, 208, 976, 2576, 5056, 8320, 12368, 17200, 22816, 29216, 36400, 44368, 53120, 62656, 72976, 84080, 95968, 108640, 122096, 136336, 151360, 167168, 183760, 201136, 219296, 238240, 257968, 278480, 299776, 321856, 344720, 368368, 392800

Offset: 1

Author

R. H. Hardin, Feb 27 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A186851.

Programs

PARI

row(4, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 07 2023

Formula

Empirical: a(n) = 392*n^2 - 1048*n + 496 for n > 3.

The above empirical formula is correct. See A186851 for details. - Andrew Howroyd, Jan 07 2023