A172964 Number of ways to place 2 nonattacking knights on an n X n cylindrical board.

0, 4, 18, 92, 230, 522, 1022, 1808, 2970, 4610, 6842, 9792, 13598, 18410, 24390, 31712, 40562, 51138, 63650, 78320, 95382, 115082, 137678, 163440, 192650, 225602, 262602, 303968, 350030, 401130, 457622, 519872, 588258, 663170, 745010, 834192, 931142, 1036298, 1150110

Offset

1,2

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^3 - 9*n + 12)/2, n>=5.

G.f.: 2*x^2*(6*x^7-30*x^6+61*x^5-66*x^4+45*x^3-21*x^2+x-2)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[2 x (6 x^7 - 30 x^6 + 61 x^5 - 66 x^4 + 45 * x^3 - 21 x^2 + x - 2) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

Crossrefs

Cf. A172529, A172132.

Sequence in context: A269450 A206639 A367875 * A317135 A196150 A185298

Adjacent sequences: A172961 A172962 A172963 * A172965 A172966 A172967

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

Status

approved