A186852 Number of 3-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.

16, 104, 328, 664, 1112, 1672, 2344, 3128, 4024, 5032, 6152, 7384, 8728, 10184, 11752, 13432, 15224, 17128, 19144, 21272, 23512, 25864, 28328, 30904, 33592, 36392, 39304, 42328, 45464, 48712, 52072, 55544, 59128, 62824, 66632, 70552, 74584, 78728, 82984, 87352

Offset

1,1

Links

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

Formula

Empirical: a(n) = 56*n^2 - 56*n - 8 for n > 1.

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

Example

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

Prog

(PARI) row(3, 40) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 07 2023

Crossrefs

Row 3 of A186851.

Sequence in context: A304505 A210687 A000739 * A010079 A022708 A328816

Adjacent sequences: A186849 A186850 A186851 * A186853 A186854 A186855

Keyword

nonn

Author

R. H. Hardin, Feb 27 2011

Extensions

Terms a(27) and beyond from Andrew Howroyd, Jan 07 2023

Status

approved