A172967 - OEIS

%I #9 Sep 12 2015 11:00:22

%S 0,0,0,208,3210,58056,458157,2524176,10587591,36576380,109008735,

%T 289450344,700477401,1570789892,3304892985,6586928032,12530769343,

%U 22891446252

%N Number of ways to place 5 nonattacking knights on an n X n cylindrical board.

%H Vincenzo Librandi, <a href="/A172967/b172967.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>

%F Explicit formula: a(n) = n*(n^9-90n^7+120n^6+3395n^5-8160n^4-62130n^3+204000n^2+463464n-1888080)/120, n>=10. For any fixed value of k > 1, a(n) = n^(2k)/k! - 9n^(2k-2)/2/(k-2)! + 6n^(2k-3)/(k-2)! + ... [_Vaclav Kotesovec_, Jan 31 2010]

%F G.f.: -x^4*(468*x^16-7964*x^15+57164*x^14-238936*x^13+664383*x^12-1323653*x^11+1986964*x^10-2334676*x^9+2209082*x^8-1718662*x^7+1118210*x^6-595746*x^5+216519*x^4-38229*x^3+34186*x^2+922*x+208)/(x-1)^11. [_Vaclav Kotesovec_, Mar 25 2010]

%t CoefficientList[Series[- x^3 (468 x^16 - 7964 x^15 + 57164 x^14 - 238936 x^13 + 664383 x^12 - 1323653 x^11 + 1986964 x^10 - 2334676 x^9 + 2209082 x^8 - 1718662 x^7 + 1118210 x^6 - 595746 x^5 + 216519 x^4 - 38229 x^3 + 34186 x^2 + 922 x + 208) / (x - 1)^11, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172532, A172136, A172964, A172965, A172966.

%K nonn,easy

%O 1,4

%A _Vaclav Kotesovec_, Feb 06 2010