|
%I #27 Mar 01 2018 15:08:18
%S 1,16,313,2320,12160,53744,209428,683524,1905625,4664384,10297579,
%T 20907590,39664250,71114916,121559433,199459466,315906248,485124352,
%U 725031335,1057839684,1510706686,2116429956,2914190277,3950340692
%N Number of ways to place 6 nonattacking bishops on a 6 X n board.
%H Vaclav Kotesovec and Vincenzo Librandi, <a href="/A172211/b172211.txt">Table of n, a(n) for n = 1..1000</a> (first 32 terms from V. Kotesovec)
%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) = (648n^6-17820n^5+240930n^4-2011545n^3+10806047n^2-35094560n+53430940)/10, n>=25.
%F For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (2k-1)/2/(k-2)!*(kn)^(k-1) + ...
%F G.f.: -x*(2*x^30-6*x^29+14*x^28-26*x^27+44*x^26-220*x^25+596*x^24-1060*x^23+1654*x^22
%F -2266*x^21+5622*x^20-13570*x^19+19848*x^18-22392*x^17+24048*x^16-30525*x^15+57673*x^14
%F -80154*x^13+61962*x^12-30874*x^11+25832*x^10-9360*x^9+16960*x^8-4710*x^7+18006*x^6+6928*x^5
%F +1968*x^4+430*x^3+222*x^2+9*x+1)/(x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[-(2 x^30 - 6 x^29 + 14 x^28 - 26 x^27 + 44 x^26 - 220 x^25 + 596 x^24 - 1060 x^23 + 1654 x^22 - 2266 x^21 + 5622 x^20 - 13570 x^19 + 19848 x^18 - 22392 x^17 + 24048 x^16 - 30525 x^15 + 57673 x^14 - 80154 x^13 + 61962 x^12 - 30874 x^11 + 25832 x^10 - 9360 x^9 + 16960 x^8 - 4710 x^7 + 18006 x^6 + 6928 x^5 + 1968 x^4 + 430 x^3 + 222 x^2 + 9 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%Y Cf. A061992, A172207, A172208, A172210.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
| 