A346391 Number of permutations f of {1,...,n} with f(n) = n and f(n-1) > f(1) such that f(1)*f(2) + ... + f(n-1)*f(n) + f(n)*f(1) == 0 (mod n^2).
0, 0, 0, 2, 17, 16, 209, 3192
Offset: 3
Examples
a(6) = 2, and 2*4 + 4*1 + 1*3 + 3*5 + 5*6 + 6*2 = 3*5 + 5*1 + 1*2 + 2*4 + 4*6 + 6*3 = 2*6^2. a(7) > 0 with 1*3 + 3*4 + 4*5 + 5*6 + 6*2 + 2*7 + 7*1 = 2*7^2. a(8) > 0 with 1*5 + 5*3 + 3*6 + 6*4 + 4*7 + 7*2 + 2*8 + 8*1 = 2*8^2. a(9) > 0 with 1*2 + 2*3 + 3*5 + 5*4 + 4*6 + 6*8 + 8*7 + 7*9 + 9*1 = 3*9^2. a(10) > 0 with 1*2 + 2*3 + 3*6 + 6*8 + 8*4 + 4*9 + 9*7 + 7*5 + 5*10 + 10*1 = 3*10^2. a(11) > 0 with 1*3 + 3*4 + 4*5 + 5*8 + 8*6 + 6*9 + 9*7 + 7*10 + 10*2 + 2*11 + 11*1 = 3*11^2.
Programs
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Mathematica
(* A program to compute a(7): *) VV[i_]:=VV[i]=Part[Permutations[{1,2,3,4,5,6}],i]; n=0;Do[If[VV[i][[1]]
Comments