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A186854
Number of 5-step knight's tours on an (n+2) X (n+2) board summed over all starting positions.
2
16, 400, 2800, 9328, 21480, 39616, 63440, 92656, 127264, 167264, 212656, 263440, 319616, 381184, 448144, 520496, 598240, 681376, 769904, 863824, 963136, 1067840, 1177936, 1293424, 1414304, 1540576, 1672240, 1809296, 1951744, 2099584, 2252816, 2411440
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 2696*n^2 - 11224*n + 9904 for n > 5.
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 1 0 2 0 0 0 0 5 0 0 0 0 1 0 0 0
0 3 0 0 0 0 0 0 3 0 0 0 0 2 0 3 0 0 0 0
0 0 0 2 0 1 0 0 0 0 4 0 0 0 0 0 0 2 5 0
0 0 4 0 0 0 0 4 0 0 0 0 3 0 1 0 4 0 0 0
0 0 0 0 5 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0
PROG
(PARI) row(5, 30) \\ row(m, n) defined in A186851. - Andrew Howroyd, Jan 07 2023
CROSSREFS
Row 5 of A186851.
Sequence in context: A269412 A269643 A071133 * A035021 A300469 A326102
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 27 2011
EXTENSIONS
Terms a(25) and beyond from Andrew Howroyd, Jan 07 2023
STATUS
approved