A172966 Number of ways to place 4 nonattacking knights on an n X n cylindrical board.
0, 0, 0, 306, 2365, 19047, 90503, 328324, 981693, 2547955, 5933257, 12681288, 25284363, 47595023, 85357395, 146879312, 243867873, 392452803, 614423653, 938708560, 1403123967, 2056426383, 2960698943, 4194107208, 5854060325
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[x^3 (76 x^13 - 684 x^12 + 2856 x^11 - 7714 x^10 + 16164 x^9 - 29151 x^8 + 45506 x^7 - 57766 x^6 + 55629 x^5 - 39385 x^4 + 21484 x^3 - 8778 x^2 + 389 x - 306) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)
Formula
a(n) = n*(n^7-54n^5+72n^4+1115n^3-2616n^2-8502n+26712)/24, n>=9.
G.f.: x^4*(76*x^13-684*x^12+2856*x^11-7714*x^10+16164*x^9-29151*x^8+45506*x^7-57766*x^6+55629*x^5-39385*x^4+21484*x^3-8778*x^2+389*x-306)/(x-1)^9. - Vaclav Kotesovec, Mar 25 2010
Extensions
More terms from Vincenzo Librandi, May 29 2013