A172234 Number of ways to place 7 nonattacking wazirs on a 7 X n board.

0, 2, 1478, 50726, 573797, 3581924, 15516804, 52550366, 149162199, 370817854, 831571604, 1717417198, 3316210152, 6054985120, 10545491888, 17638773534, 28489610297, 44631652698, 68064067456, 101350519742, 147731315314, 211249526076, 296891922604, 410745537182

Offset

1,2

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)

Formula

a(n) = (117649*n^7-1663893*n^6+10942729*n^5-43685355*n^4+114945646*n^3-199980312*n^2+213228096*n-107390880)/720, n>=6.

For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(5k-2)/2/k!*(kn)^(k-1) + ...

G.f.: x^2*(7*x^11-48*x^10+370*x^9+40*x^8+8541*x^7+45282*x^6+190420*x^5 +329248*x^4+209261*x^3+38958*x^2+1462*x+2)/(x-1)^8. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[x (7 x^11 - 48 x^10 + 370 x^9 + 40 x^8 + 8541 x^7 + 45282 x^6 + 190420 x^5 + 329248 x^4 + 209261 x^3 + 38958 x^2 + 1462 x+2) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

Crossrefs

Cf. A172229, A172230, A172231, A172232, A061993.

Sequence in context: A170993 A259323 A172939 * A339543 A023291 A319329

Adjacent sequences: A172231 A172232 A172233 * A172235 A172236 A172237

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Extensions

More terms from Vincenzo Librandi, May 29 2013

Status

approved