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

1,3

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)(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

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 *)

Crossrefs

Cf. A172530, A172134, A172964.

Sequence in context: A256275 A235346 A077231 * A002022 A065948 A367776

Adjacent sequences: A172962 A172963 A172964 * A172966 A172967 A172968

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

Status

approved