|
%I #18 Apr 11 2024 13:59:41
%S 0,0,0,114,14650,368868,4216498,30222074,158918030,669582340,
%T 2387463550,7470004954,21036576578,54315955588,130382565930,
%U 294116445082,628800849110,1282821452132,2511317339446,4739431178170
%N Number of ways to place 6 nonattacking wazirs on an n X n board.
%C Wazir is a (fairy chess) leaper [0,1].
%H Vincenzo Librandi, <a href="/A178409/b178409.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>, 6ed, 2013
%F Explicit formula: a(n) = 1/720 * (n^12 -75*n^10 +60*n^9 +2365*n^8 -3720*n^7 -38085*n^6 +89580*n^5 +292834*n^4 -984960*n^3 -552240*n^2 +4128960*n -3160800), n >= 5.
%F G.f.: -2*x^4 * (4*x^13 -17*x^12 +3*x^11 -469*x^10 +4084*x^9 -10233*x^8 -3482*x^7 +66494*x^6 -125152*x^5 +35457*x^4 +265655*x^3 +93655*x^2 +6584*x +57)/(x-1)^13.
%F a(n) = A232833(n,6). - _R. J. Mathar_, Apr 11 2024
%t CoefficientList[Series[- 2 x^3 (4 x^13 - 17 x^12 + 3 x^11 - 469 x^10 + 4084 x^9 - 10233 x^8 - 3482 x^7 + 66494 x^6 - 125152 x^5 + 35457 x^4 + 265655 x^3 + 93655 x^2 + 6584 x + 57) / (x - 1)^13, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y Cf. A172225, A172226, A172227, A172228.
%K nonn,easy,changed
%O 1,4
%A _Vaclav Kotesovec_, May 27 2010
|
