A174698 - OEIS

%I #13 Sep 12 2015 11:00:23

%S 1,81,4409,175720,2479881,17925691,92952858,379978716,1286959255,

%T 3765248749,9805497200,23226916560,50866495373,104288896551,

%U 202154535834,373400685738,661407061211,1129334088897,1866838857216

%N Number of ways to place 8 nonattacking knights on an 8 X n board.

%H Vincenzo Librandi, <a href="/A174698/b174698.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) = (262144*n^8 -6881280*n^7+93456384*n^6 -838693632*n^5 +5361604836*n^4 -24739168020*n^3+79766188151*n^2 -163079018193*n +160750559340)/630, n>=14.

%F G.f.: x*(592*x^21 -584*x^20 -18100*x^19 +49628*x^18+134264*x^17 -735838*x^16 +584418*x^15+2607764*x^14 -7093608*x^13 +5656936*x^12 +5136811*x^11 -13973779*x^10 +14583702*x^9 -1612610*x^8 +2009820*x^7 +6682287*x^6 +1572406*x^5 +1050447*x^4 +138871*x^3+3716*x^2 +72*x+1)/(1-x)^9.

%t CoefficientList[Series[(592 x^21 - 584 x^20 - 18100 x^19 + 49628 x^18 + 134264 x^17 - 735838 x^16 + 584418 x^15 + 2607764 x^14 - 7093608 x^13 + 5656936 x^12 + 5136811 x^11 - 13973779 x^10 + 14583702 x^9 - 1612610 x^8 + 2009820 x^7 + 6682287 x^6 + 1572406 x^5 + 1050447 x^4 + 138871 x^3 + 3716 x^2 + 72 x + 1) / (1 - x)^9, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 30 2013 *)

%Y Cf. A172449, A172212, A172213, A172214, A172215, A172217.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Mar 27 2010