A172223 Number of ways to place 5 nonattacking zebras on a 5 X n board.

1, 252, 1925, 6534, 20502, 57710, 142312, 308254, 606051, 1105332, 1897899, 3100250, 4857000, 7344010, 10771530, 15387310, 21479725, 29380900, 39469835, 52175530, 67980110, 87421950, 111098800, 139670910, 173864155

Offset

1,2

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

Eric Weisstein's World of Mathematics, Zebra Graph

Wikipedia, Zebra (chess)

Formula

a(n) = 5*(125n^5-1250n^4+7575n^3-28426n^2+64000n-67056)/24, n>=12.

G.f.: x * (14*x^16 -32*x^15 +14*x^14 -292*x^13 +898*x^12 -536*x^11 +514*x^10 -4232*x^9 +7258*x^8 -3296*x^7 +266*x^6 -2018*x^5 +5148*x^4 -1256*x^3 +428*x^2 +246*x +1) / (x-1)^6. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[(14 x^16 - 32 x^15 + 14 x^14 - 292 x^13 + 898 x^12 - 536 x^11 + 514 x^10 - 4232 x^9 + 7258 x^8 - 3296 x^7 + 266 x^6 - 2018 x^5 + 5148 x^4 - 1256 x^3 + 428 x^2 + 246 x+1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A172140, A061991, A172221, A172222.

Sequence in context: A184499 A154045 A364687 * A154073 A166783 A104679

Adjacent sequences: A172220 A172221 A172222 * A172224 A172225 A172226

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved