A172533 - OEIS

%I #13 Feb 20 2018 15:02:11

%S 0,0,0,56,0,54972,764596,8972896,62560728,322246800,1323868260,

%T 4595943336,14000143196,38413461800,96746410800,226834407552,

%U 500492572112,1048044384360,2096986629308,4031211268200

%N Number of ways to place 6 nonattacking knights on an n X n toroidal board.

%H Vincenzo Librandi, <a href="/A172533/b172533.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 a(n) = n^2*(n^10-135n^8+8005n^6-262665n^4+4816354n^2-39858840)/720, n>=13.

%F G.f.: 4*x^4*(240*x^21-3120*x^20+20470*x^19-105106*x^18+512024*x^17-2216597*x^16+7650408*x^15-20251702*x^14+41149629*x^13-64905350*x^12+80399423*x^11-78967736*x^10+61875645*x^9-38631940*x^8+19002633*x^7-7392461*x^6+2560624*x^5-840251*x^4-8486*x^3-14835*x^2+182*x-14)/(x-1)^13. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[4 x^3 (240 x^21 - 3120 x^20 + 20470 x^19 - 105106 x^18 + 512024 x^17 - 2216597 x^16 + 7650408 x^15 - 20251702 x^14 + 41149629 x^13 - 64905350 x^12 + 80399423 x^11 - 78967736 x^10 + 61875645 x^9 - 38631940 x^8 + 19002633 x^7 - 7392461 x^6 + 2560624 x^5 - 840251 x^4 - 8486 x^3 - 14835 x^2 + 182 x - 14) / (x - 1)^13,{x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172529, A172530, A172531, A172532.

%K nonn,easy

%O 1,4

%A _Vaclav Kotesovec_, Feb 06 2010