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%I #10 Aug 19 2019 16:50:07
%S 0,0,0,0,23,1104,16945,141696,810746,3568352,12948318,40514560,
%T 112720393,285073712,666143975,1456288512,3007576740,5913372864,
%U 11138305068,20202100224,35433809451,60316600080,99947225741,161638967424,255701773822,396439174560,603407582570
%N Number of ways to place 5 nonattacking semi-queens on an n X n board.
%C Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.
%H Michael De Vlieger, <a href="/A202656/b202656.txt">Table of n, a(n) for n = 1..10000</a>
%H Christopher R. H. Hanusa, Thomas Zaslavsky, <a href="https://arxiv.org/abs/1906.08981">A q-queens problem. VII. Combinatorial types of nonattacking chess riders</a>, arXiv:1906.08981 [math.CO], 2019.
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%F a(n) = n^10/120 - 2*n^9/9 + 95*n^8/36 - 183*n^7/10 + 14663*n^6/180 - 1201*n^5/5 + 16753*n^4/36 - 25364*n^3/45 + 68293*n^2/180 - 12781*n/120 + (n^3/2 - 6*n^2 + 39*n/2 - 61/4)*floor(n/2).
%F G.f.: -x^5*(1899*x^9 + 16515*x^8 + 60512*x^7 + 116784*x^6 + 137646*x^5 + 98222*x^4 + 41688*x^3 + 9608*x^2 + 943*x + 23)/((x-1)^11*(x+1)^4).
%t Rest@ CoefficientList[Series[-x^5*(1899 x^9 + 16515 x^8 + 60512 x^7 + 116784 x^6 + 137646 x^5 + 98222 x^4 + 41688 x^3 + 9608 x^2 + 943 x + 23)/((x - 1)^11*(x + 1)^4), {x, 0, 27}], x] (* _Michael De Vlieger_, Aug 19 2019 *)
%Y Cf. A099152, A108792, A103220, A202654, A202655, A202657.
%K nonn
%O 1,5
%A _Vaclav Kotesovec_, Dec 22 2011
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