A172231 Number of ways to place 5 nonattacking wazirs on a 5 X n board.

0, 2, 174, 1998, 10741, 38438, 107004, 251354, 522528, 990816, 1748883, 2914894, 4635639, 7089658, 10490366, 15089178, 21178634, 29095524, 39224013, 51998766

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

Wazir is a (fairy chess) leaper [0,1].

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, Grid Graph
• Wikipedia, Wazir (chess)

Crossrefs

Cf. A172228, A172229, A172230, A061991.

Programs

Mathematica

CoefficientList[Series[x (5 x^7 + 8 x^6 + 129 x^5 + 512 x^4 + 1323 x^3 + 984 x^2 + 162 x + 2) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (625*n^5-5750*n^4+23535*n^3-54202*n^2+70640*n-41616)/24, n>=4.

G.f.: x^2*(5*x^7+8*x^6+129*x^5+512*x^4+1323*x^3+984*x^2+162*x+2)/(x-1)^6. - Vaclav Kotesovec, Mar 25 2010