A173775 Number of ways to place 5 nonattacking queens on an n X n toroidal board.
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
Offset: 1
Links
Formula
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).