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A348183 a(n) is the determinant of the n X n matrix M = (m_{i,j}), i,j from 0 to n-1: m{i,j} = (i+j)^2 mod n.

%I A348183 #35 Jan 02 2024 16:13:00
%S A348183 1,0,-1,-2,0,250,5616,-33614,0,204073344,-900000000,-9431790764,0,
%T A348183 10752962364222,-1870899108384768,-36328974609375000,0,
%U A348183 22899384412078526344,-111400529859275793629184,-43843094862278417487512,0,2870507605405055660542502550,67015802375208384199755038720
%N A348183 a(n) is the determinant of the n X n matrix M = (m_{i,j}), i,j from 0 to n-1: m{i,j} = (i+j)^2 mod n.
%C A348183 It seems that for values of n divisible by 4 -> a(n) = 0 and rank(M) = n/2.
%e A348183 a(2) =  |0^2 mod 2, 1^2 mod 2| = -1
%e A348183         |1^2 mod 2, 2^2 mod 2|
%e A348183 --
%e A348183         |0^2 mod 3, 1^2 mod 3, 2^2 mod 3|
%e A348183 a(3) =  |1^2 mod 3, 2^2 mod 3, 3^2 mod 3| = -2
%e A348183         |2^2 mod 3, 3^2 mod 3, 4^2 mod 3|
%t A348183 a[n_]:=Table[Mod[(i+j)^2,n],{i,0,n-1},{j,0,n-1}]; Join[{1},Table[Det[a[n]], {n, 22}]] (* _Stefano Spezia_, Oct 06 2021 *)
%o A348183 (PARI) a(n) = matdet(matrix(n, n, i, j, i--; j--; (i+j)^2 % n)); \\ _Michel Marcus_, Oct 06 2021
%o A348183 (Python)
%o A348183 from sympy import Matrix
%o A348183 def A348183(n): return Matrix(n,n,[pow(i+j,2,n) for i in range(n) for j in range(n)]).det() # _Chai Wah Wu_, Nov 24 2021
%Y A348183 Cf. A070896.
%K A348183 sign
%O A348183 0,4
%A A348183 _Dennis Gruhlke_ and _Albert Böschow_, Oct 05 2021
%E A348183 a(14)-a(17) corrected by and more terms from _Stefano Spezia_, Oct 06 2021.