A172140 Number of ways to place 5 nonattacking zebras on an n X n board.

0, 0, 126, 2032, 20502, 160696, 929880, 4117520, 15037036, 47368960, 132577826, 336828368, 789558314, 1729320120, 3574328936, 7027309888, 13226773092, 23959787480, 41954706558, 71276149776, 117848892710, 190142197976

Offset

1,3

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n) = (n^10 - 90*n^8 + 400*n^7 + 2915*n^6 - 26880*n^5 + 2430*n^4 + 609920*n^3 - 1517496*n^2 - 4188480*n + 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[2x^2(100x^19 -648x^18 +1450x^17 -2126x^16 +10452x^15 - 43872x^14 +92798x^13 -100834x^12 +56460x^11 -61636x^10 +182288x^9 -303224x^8 + 275038x^7 -128982x^6 +21681x^5 +1933x^4 -13072x^3 -2540x^2 -323x-63)/(x-1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

Prog

(SageMath) [0, 0, 126, 2032, 20502, 160696, 929880, 4117520, 15037036, 47368960, 132577826] + [(n^10 -90*n^8 +400*n^7 +2915*n^6 -26880*n^5 +2430*n^4 +609920*n^3 - 1517496*n^2 -4188480*n +16581120)/120 for n in (12..50)] # G. C. Greubel, Apr 19 2022

Crossrefs

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

Sequence in context: A304559 A189345 A255177 * A331100 A196414 A133499

Adjacent sequences: A172137 A172138 A172139 * A172141 A172142 A172143

Keyword

nonn

Author

Vaclav Kotesovec, Jan 26 2010

Status

approved