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A348183
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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.
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1
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1, 0, -1, -2, 0, 250, 5616, -33614, 0, 204073344, -900000000, -9431790764, 0, 10752962364222, -1870899108384768, -36328974609375000, 0, 22899384412078526344, -111400529859275793629184, -43843094862278417487512, 0, 2870507605405055660542502550, 67015802375208384199755038720
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OFFSET
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0,4
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COMMENTS
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It seems that for values of n divisible by 4 -> a(n) = 0 and rank(M) = n/2.
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LINKS
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EXAMPLE
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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|
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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a(14)-a(17) corrected by and more terms from Stefano Spezia, Oct 06 2021.
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STATUS
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approved
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