A172221 Number of ways to place 3 nonattacking zebras on a 3 X n board.

1, 20, 84, 200, 403, 720, 1180, 1808, 2631, 3676, 4970, 6540, 8413, 10616, 13176, 16120, 19475, 23268, 27526, 32276, 37545, 43360, 49748, 56736, 64351, 72620, 81570, 91228, 101621, 112776, 124720, 137480, 151083, 165556, 180926, 197220

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) = (9*n^3 - 21*n^2 + 50*n - 48)/2, n>=6.

G.f.: x*(2*x^8-4*x^7+2*x^6-8*x^5+28*x^4-20*x^3+10*x^2+16*x+1)/(x-1)^4. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[(2 x^8 - 4 x^7 + 2 x^6 - 8 x^5 + 28 x^4 - 20 x^3 + 10 x^2 + 16 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Crossrefs

Cf. A172138, A061989.

Sequence in context: A156389 A044207 A044588 * A006566 A205312 A268888

Adjacent sequences: A172218 A172219 A172220 * A172222 A172223 A172224

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Extensions

More terms from Vincenzo Librandi, May 28 2013

Status

approved