A188779 Number of 4-turn bishop's tours on an n X n board summed over all starting positions.
0, 0, 24, 328, 1720, 5816, 15424, 34736, 69776, 128528, 221448, 361528, 564872, 850696, 1241968, 1765344, 2451872, 3336864, 4460664, 5868456, 7611096, 9744856, 12332320, 15442064, 19149616, 23537072, 28694120, 34717592, 41712552, 49791784
Offset: 1
Keywords
Examples
Some solutions for 4X4 ..0..0..0..1....0..0..0..0....0..0..1..0....0..0..0..0....0..4..0..1 ..0..0..3..0....1..0..0..0....0..4..0..2....0..4..0..2....3..0..0..0 ..0..4..0..0....0..2..0..4....0..0..3..0....0..0..3..0....0..2..0..0 ..2..0..0..0....0..0..3..0....0..0..0..0....0..1..0..0....0..0..0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..42
Formula
Empirical: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)
Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)
Empirical: G.f.: 8*x^3*(3 + 29*x + 63*x^2 + 43*x^3 + 14*x^4)/((1-x)^6*(1+x)^2)
Empirical: a(n) = -2 + 257*n/15 - 109*n^2/3 + 106*n^3/3 - 47*n^4/3 + 38*n^5/15 + (-1)^n*(2-n)
(End)
Comments