A172531 Number of ways to place 4 nonattacking knights on an n X n toroidal board.

0, 0, 0, 228, 600, 12357, 68796, 275888, 872532, 2344025, 5580762, 12107196, 24392446, 46261537, 83426400, 144157632, 240119696, 387393921, 607715342, 929951100

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^2*(n^6 - 54*n^4 + 1115*n^2 - 8934)/24, n>=9.

G.f.: x^4 * (192*x^13 -1728*x^12 +7452*x^11 -21238*x^10 +46658*x^9 -84582*x^8 +125397*x^7 -144875*x^6 +124920*x^5 -79904*x^4 +39969*x^3 -15165*x^2 +1452*x -228) / (x-1)^9. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[x^3 (192 x^13 - 1728 x^12 + 7452 x^11 - 21238 x^10 + 46658 x^9 - 84582 x^8 + 125397 x^7 - 144875 x^6 + 124920 x^5 - 79904 x^4 + 39969 x^3 - 15165 x^2 + 1452 x - 228) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

Crossrefs

Cf. A172529, A172530, A172135, A172519.

Sequence in context: A154519 A128808 A043411 * A258557 A206005 A228963

Adjacent sequences: A172528 A172529 A172530 * A172532 A172533 A172534

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Status

approved