A201548 - OEIS

%I #13 Sep 12 2015 11:00:28

%S 0,0,0,0,10,308574,81442802,5296005568,146127335256,2309813476870,

%T 24738873315596,198759048859008,1279605298916568,6906427308782106,

%U 32277449304595350,133788325435448576,500896430870051174,1718268150463137018,5462521782760829320,16243031089247644800

%N Number of ways to place 10 nonattacking wazirs on an n X n toroidal board.

%C Wazir is a leaper [0,1].

%H Vincenzo Librandi, <a href="/A201548/b201548.txt">Table of n, a(n) for n = 1..1000</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>

%F Explicit formula: n^20/3628800 - n^18/16128 + 773*n^16/120960 - 761*n^14/1920 + 2820613*n^12/172800 - 356093*n^10/768 + 412940467*n^8/45360 - 2408161207*n^6/20160 + 24029851729*n^4/25200 - 3541971*n^2, n>=11.

%F G.f.: 2*x^5*(10*x^26 - 615*x^25 + 14637*x^24 - 193410*x^23 + 1669110*x^22 - 10270682*x^21 + 47718030*x^20 - 174153546*x^19 + 511148331*x^18 - 1213451007*x^17 + 2302816572*x^16 - 3418379599*x^15 + 4006461091*x^14 - 4626995415*x^13 + 8410419611*x^12 - 19068629603*x^11 + 33871890471*x^10 - 39181017568*x^9 + 18018811352*x^8 - 5120263515*x^7 - 178499919965*x^6 - 123414145507*x^5 - 25801931589*x^4 - 1825246983*x^3 - 37482424*x^2 - 154182*x - 5)/(x-1)^21.

%t CoefficientList[Series[2 x^4 (10 x^26 - 615 x^25 + 14637 x^24 - 193410 x^23 + 1669110 x^22 - 10270682 x^21 + 47718030 x^20 - 174153546 x^19 + 511148331 x^18 - 1213451007 x^17 + 2302816572 x^16 - 3418379599 x^15 + 4006461091 x^14 - 4626995415 x^13 + 8410419611 x^12 - 19068629603 x^11 + 33871890471 x^10 - 39181017568 x^9 + 18018811352 x^8 - 5120263515 x^7 - 178499919965 x^6 - 123414145507 x^5 - 25801931589 x^4 - 1825246983 x^3 - 37482424 x^2-154182 x - 5) / (x - 1)^21, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 04 2013 *)

%Y Cf. A201236, A201237, A201238, A201239, A201240, A201241, A201242, A201547.

%K nonn,easy

%O 1,5

%A _Vaclav Kotesovec_, Dec 02 2011