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%I #16 Apr 23 2023 20:17:11
%S 1,12,143,770,3368,12632,38566,98968,222351,450682,843169,1479116,
%T 2460912,3917228,6006056,8917888,12878847,18153806,25049515,33917724,
%U 45158308,59222392,76615476,97900560,123701269,154704978,191665937,235408396,286829730,346903564
%N Number of ways to place 5 nonattacking bishops on a 5 X n board.
%H Vincenzo Librandi, <a href="/A172210/b172210.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>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = (625n^5-11250n^4+98875n^3-515250n^2+1566016n-2194944)/24, n>=16.
%F G.f.: x*(2*x^20 -4*x^19 +8*x^18 -12*x^17 -48*x^16 +140*x^15 -158*x^14 +208*x^13 +134*x^12 -932*x^11 +1048*x^10 -182*x^9 +436*x^8 +396*x^7 -32*x^6 +1288*x^5 +668*x^4 +72*x^3 +86*x^2 +6*x+1)/(x-1)^6. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[(2 x^20 - 4 x^19 + 8 x^18 - 12 x^17 - 48 x^16 + 140 x^15 - 158 x^14 + 208 x^13 + 134 x^12 - 932 x^11 + 1048*x^10 -182*x^9+ 436 * x^8 + 396 x^7 - 32 x^6 + 1288 * x^5 + 668 * x^4 + 72 * x^3 + 86 * x^2 + 6 * x + 1) / (x - 1)^6, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%Y Cf. A172129, A061991, A172207, A172208.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
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