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A173775
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Number of ways to place 5 nonattacking queens on an n X n toroidal board
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6
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0, 0, 0, 0, 10, 0, 882, 13312, 85536, 561440, 2276736, 9471744, 27991470, 85725696, 209107890, 525062144, 1116665944, 2437807104, 4691672964, 9234168960, 16462896030, 29919532544, 50215537658, 85687824384, 136944081500
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = 1/120*n^10-1/3*n^9 + 143/24*n^8-373/6*n^7 + 99377/240*n^6-3603/2*n^5 + 119627/24*n^4-23833/3*n^3 + 16342/3*n^2 + (1/24*n^8-3/2*n^7 + 1111/48*n^6-391/2*n^5 + 7595/8*n^4-2487*n^3 + 8032/3*n^2)*(-1)^n + (9/2*n^4-78*n^3 + 374*n^2)*cos(Pi*n/2) + (8/3*n^4-128/3*n^3 + 656/3*n^2)*cos(2*Pi*n/3) + 80/3*n^2*cos(Pi*n/3) + 16/5*n^2*cos(2*Pi*n/5) + 16/5*n^2*cos(Pi*n/5)*(-1)^n.
Recurrence: a(n) = -3a(n-1)-5a(n-2)-5a(n-3) + 2a(n-4) + 17a(n-5) + 37a(n-6) + 49a(n-7) + 35a(n-8)-16a(n-9)-101a(n-10)-185a(n-11)-215a(n-12)-139a(n-13) + 56a(n-14) + 321a(n-15) + 544a(n-16) + 588a(n-17) + 368a(n-18)-99a(n-19)-656a(n-20)-1069a(n-21)-1111a(n-22)-689a(n-23) + 84a(n-24) + 929a(n-25) + 1488a(n-26) + 1506a(n-27) + 939a(n-28)-939a(n-30)-1506a(n-31)-1488a(n-32)-929a(n-33)-84a(n-34) + 689a(n-35) + 1111a(n-36) + 1069a(n-37) + 656a(n-38) + 99a(n-39)-368a(n-40)-588a(n-41)-544a(n-42)-321a(n-43)-56a(n-44) + 139a(n-45) + 215a(n-46) + 185a(n-47) + 101a(n-48) + 16a(n-49)-35a(n-50)-49a(n-51)-37a(n-52)-17a(n-53)-2a(n-54) + 5a(n-55) + 5a(n-56) + 3a(n-57) + a(n-58).
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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