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A172136 Number of ways to place 5 nonattacking knights on an n X n board. 10
0, 0, 2, 340, 9386, 97580, 649476, 3184708, 12472084, 41199404, 119171110, 309957412, 739123094, 1639655452, 3422020324, 6778432292, 12833460256, 23356032940, 41051290730, 69954580804 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For any fixed value of k>1, a(n) = n^(2k) /k! - 9n^(2k - 2) /2/(k - 2)! + 12n^(2k - 3) /(k - 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

Explicit formula: a(n) = (n^10 - 90n^8 + 240n^7 + 3235n^6 - 16320n^5 - 40530n^4 + 396480n^3 - 231656n^2 - 3359520n + 6509280)/120, n >= 8.

G.f.: 2*x^3 * (74*x^15 -518*x^14 +1110*x^13 +1046*x^12 -11332*x^11 +29950*x^10 -42430*x^9 +32476*x^8 -11684*x^7 -1000*x^6 +15021*x^5 -18443*x^4 -6352*x^3 -2878*x^2 -159*x -1) / (x-1)^11. [Vaclav Kotesovec, Mar 25 2010]

MATHEMATICA

CoefficientList[Series[2 x^2 (74 x^15 - 518 x^14 + 1110  x^13 + 1046 x^12 - 11332 x^11 + 29950 x^10 - 42430 x^9 + 32476 x^8 - 11684 x^7 - 1000 x^6 + 15021 x^5 - 18443 x^4 - 6352 x^3 - 2878 x^2 - 159 x - 1) / (x-1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A108792, A172129, A172132, A172134, A172135.

Column k=5 of A244081.

Sequence in context: A057626 A201310 A063968 * A248172 A064501 A063831

Adjacent sequences:  A172133 A172134 A172135 * A172137 A172138 A172139

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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