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A172531 Number of ways to place 4 nonattacking knights on an n X n toroidal board. 5
0, 0, 0, 228, 600, 12357, 68796, 275888, 872532, 2344025, 5580762, 12107196, 24392446, 46261537, 83426400, 144157632, 240119696, 387393921, 607715342, 929951100 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)