A172234 - OEIS

%I #14 Feb 20 2018 14:31:31

%S 0,2,1478,50726,573797,3581924,15516804,52550366,149162199,370817854,

%T 831571604,1717417198,3316210152,6054985120,10545491888,17638773534,

%U 28489610297,44631652698,68064067456,101350519742,147731315314,211249526076,296891922604,410745537182

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

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

%H Vincenzo Librandi, <a href="/A172234/b172234.txt">Table of n, a(n) for n = 1..1000</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wazir_(chess)">Wazir (chess)</a>

%F 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.

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

%F 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

%t 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 *)

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

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Jan 29 2010

%E More terms from _Vincenzo Librandi_, May 29 2013