A172965 Number of ways to place 3 nonattacking knights on an n X n cylindrical board.
0, 0, 6, 240, 1010, 4056, 12068, 30000, 65628, 130480, 240856, 418968, 694200, 1104488, 1697820, 2533856, 3685668, 5241600, 7307248, 10007560, 13489056, 17922168, 23503700, 30459408, 39046700, 49557456, 62320968, 77707000, 96128968, 118047240, 143972556
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
Programs
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Mathematica
CoefficientList[Series[- 2 x^2 (15 x^9 - 141 x^8 + 564 x^7 - 1276 x^6 + 1812 x^5 - 1652 x^4 + 908 x^3 - 272 x^2 + 99 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2013 *)
Formula
a(n) = n*(n - 3)(n^4 + 3*n^3 - 18*n^2 - 18*n + 164)/6, n>=6.
G.f.: -2*x^3*(15*x^9-141*x^8+564*x^7-1276*x^6+1812*x^5-1652*x^4+908*x^3-272*x^2+99*x+3)/(x-1)^7. - Vaclav Kotesovec, Mar 25 2010
Extensions
More terms from Vincenzo Librandi, May 29 2013