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A228549
Determinant of the n X n matrix with (i,j)-entry equal to 1 or 0 according as i + j is squarefree or not.
5
1, -1, -2, 3, 2, -1, -5, 25, -20, -16, -7, 23, -39, 25, 309, 455, 901, -2168, 920, 1047, 2302, -1536, 3272, 161162, -289493, -529263, 1418949, -1562590, -579999, 15145, 5844471, 5244416, -65749104, 176617384, 2077411081, 7381004327, 10211507191, -10333531933, 7086785521, 8502336136
OFFSET
1,3
COMMENTS
Conjecture: a(n) is always nonzero. Moreover, |a(n)|^(1/n) tends to infinity.
We have verified that a(n) is nonzero for all n <= 500.
LINKS
EXAMPLE
a(1) = 1 since 1 + 1 = 2 is squarefree.
MATHEMATICA
a[n_]:=a[n]=Det[Table[If[SquareFreeQ[i+j]==True, 1, 0], {i, 1, n}, {j, 1, n}]]
Table[a[n], {n, 1, 20}]
Table[With[{nn=x}, Det[Table[If[SquareFreeQ[i+j], 1, 0], {i, nn}, {j, nn}]]], {x, 40}] (* Harvey P. Dale, Apr 02 2023 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Zhi-Wei Sun, Aug 25 2013
STATUS
approved