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

1,1

Links

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

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

Example

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

Prog

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

Crossrefs

Row 4 of A186851.

Sequence in context: A016217 A055758 A046088 * A016159 A297370 A285167

Adjacent sequences: A186850 A186851 A186852 * A186854 A186855 A186856

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Status

approved