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A172140 Number of ways to place 5 nonattacking zebras on an n X n board. 4
0, 0, 126, 2032, 20502, 160696, 929880, 4117520, 15037036, 47368960, 132577826, 336828368, 789558314, 1729320120, 3574328936, 7027309888, 13226773092, 23959787480, 41954706558, 71276149776, 117848892710, 190142197976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Zebra is a (fairy chess) leaper [2,3].

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^10 - 90n^8 + 400n^7 + 2915n^6 - 26880n^5 + 2430n^4 + 609920n^3 - 1517496n^2 - 4188480n + 16581120)/120, n >= 12.

For any fixed value of k > 1, a(n) = n^(2k) /k! - 9n^(2k - 2) /2/(k - 2)! + 20n^(2k - 3) /(k - 2)! + ...

G.f.: 2*x^3 * (100*x^19 -648*x^18 +1450*x^17 -2126*x^16 +10452*x^15 -43872*x^14 +92798*x^13 -100834*x^12 +56460*x^11 -61636*x^10 +182288*x^9 -303224*x^8 +275038*x^7 -128982*x^6 +21681*x^5 +1933*x^4 -13072*x^3 -2540*x^2 -323*x -63) / (x-1)^11. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

CoefficientList[Series[2 x^2 (100 x^19 - 648 x^18 + 1450 x^17 - 2126 x^16 + 10452 x^15 - 43872 x^14 + 92798 x^13 - 100834 x^12 + 56460 x^11 - 61636 x^10 + 182288 x^9 - 303224 x^8 + 275038 x^7 - 128982 x^6 + 21681 x^5 + 1933 x^4 - 13072 x^3 - 2540 x^2 - 323 x-63) / (x - 1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

Cf. A108792, A172129, A172136, A172137, A172138, A172139.

Sequence in context: A304559 A189345 A255177 * A196414 A133499 A219005

Adjacent sequences:  A172137 A172138 A172139 * A172141 A172142 A172143

KEYWORD

nonn

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.)