OFFSET
0,4
COMMENTS
It seems that for values of n divisible by 4 -> a(n) = 0 and rank(M) = n/2.
EXAMPLE
a(2) = |0^2 mod 2, 1^2 mod 2| = -1
|1^2 mod 2, 2^2 mod 2|
--
|0^2 mod 3, 1^2 mod 3, 2^2 mod 3|
a(3) = |1^2 mod 3, 2^2 mod 3, 3^2 mod 3| = -2
|2^2 mod 3, 3^2 mod 3, 4^2 mod 3|
MATHEMATICA
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 *)
PROG
(PARI) a(n) = matdet(matrix(n, n, i, j, i--; j--; (i+j)^2 % n)); \\ Michel Marcus, Oct 06 2021
(Python)
from sympy import Matrix
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
CROSSREFS
KEYWORD
sign
AUTHOR
Dennis Gruhlke and Albert Böschow, Oct 05 2021
EXTENSIONS
a(14)-a(17) corrected by and more terms from Stefano Spezia, Oct 06 2021.
STATUS
approved