A172530 Number of ways to place 3 nonattacking knights on an n X n toroidal board.

0, 0, 6, 208, 600, 3252, 10584, 27584, 61992, 125300, 233772, 409584, 682084, 1089172, 1678800, 2510592, 3657584, 5208084, 7267652, 9961200, 13435212, 17860084, 23432584, 30378432, 38955000, 49454132, 62205084

Offset: 1

Author

Vaclav Kotesovec, Feb 06 2010

Keywords

• nonn
• easy

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

Crossrefs

Cf. A172529, A172134, A172518.

Programs

Mathematica

CoefficientList[Series[- 2 x^2 (50 x^9 - 398 x^8 + 1425 x^7 - 2989 x^6 + 3971 x^5 - 3325 x^4 + 1605 x^3 - 365 x^2 + 83 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2013 *)

Formula

a(n) = n^2*(n^4 - 27*n^2 + 218)/6, n>=6.

G.f.: -2*x^3 * (50*x^9 -398*x^8 +1425*x^7 -2989*x^6 +3971*x^5 -3325*x^4 +1605*x^3 -365*x^2 +83*x +3) / (x-1)^7. - Vaclav Kotesovec, Mar 25 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013