A172222 Number of ways to place 4 nonattacking zebras on a 4 X n board.

1, 70, 406, 1168, 2948, 6576, 13122, 23808, 40168, 63996, 97344, 142516, 202072, 278828, 375856, 496484, 644296, 823132, 1037088, 1290516, 1588024, 1934476, 2334992, 2794948, 3319976

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A172139, A061990, A172221.

Programs

Mathematica

CoefficientList[Series[-(4 x^12 - 6 x^11 - 2 x^10 - 52 x^9 + 160 x^8 - 88 x^7 + 2 x^6 - 195 x^5 + 473 x^4 - 172 x^3 + 66 x^2 + 65 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = 4*(8*n^4 - 48*n^3 + 202*n^2 - 471*n + 507)/3, n>=9.

G.f.: -x * (4*x^12 -6*x^11 -2*x^10 -52*x^9 +160*x^8 -88*x^7 +2*x^6 -195*x^5 +473*x^4 -172*x^3 +66*x^2 +65*x +1) / (x-1)^5. - Vaclav Kotesovec, Mar 25 2010