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A202656
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Number of ways to place 5 nonattacking semi-queens on an n X n board.
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5
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0, 0, 0, 0, 23, 1104, 16945, 141696, 810746, 3568352, 12948318, 40514560, 112720393, 285073712, 666143975, 1456288512, 3007576740, 5913372864, 11138305068, 20202100224, 35433809451, 60316600080, 99947225741, 161638967424, 255701773822, 396439174560, 603407582570
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OFFSET
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1,5
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COMMENTS
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Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.
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LINKS
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FORMULA
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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).
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).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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