login
A187049
Number of 5-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.
1
0, 0, 8, 456, 2896, 9216, 20648, 37472, 59524, 86656, 118868, 156160, 198532, 245984, 298516, 356128, 418820, 486592, 559444, 637376, 720388, 808480, 901652, 999904, 1103236, 1211648, 1325140, 1443712, 1567364, 1696096, 1829908, 1968800, 2112772
OFFSET
1,3
COMMENTS
Row 5 of A187046.
LINKS
FORMULA
Empirical: a(n) = 2540*n^2 - 21128*n + 43936 for n>7.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 4*x^3*(2 + 108*x + 388*x^2 + 472*x^3 + 308*x^4 + 70*x^5 - 41*x^6 - 37*x^7) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
(End)
EXAMPLE
Some solutions for 4 X 4:
..0..0..0..0....0..0..0..0....0..0..3..0....4..0..0..0....0..5..0..1
..0..0..1..0....0..4..0..0....0..2..0..4....0..5..0..1....0..0..0..0
..0..4..0..2....3..0..1..0....0..0..0..0....0..0..3..0....0..2..0..4
..5..0..3..0....0..2..0..5....0..5..0..1....0..2..0..0....0..0..3..0
CROSSREFS
Cf. A187046.
Sequence in context: A042525 A028449 A209840 * A367707 A221157 A015006
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 02 2011
STATUS
approved