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

1,4

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

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

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 *)

Crossrefs

Cf. A172531, A172135, A172964, A172965.

Sequence in context: A158589 A030030 A206679 * A223073 A064257 A221854

Adjacent sequences: A172963 A172964 A172965 * A172967 A172968 A172969

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

Status

approved