OFFSET
1,17
COMMENTS
Conjecture: a(n) is nonzero for any n > 21.
Zhi-Wei Sun also made the following similar conjecture:
Let A(n) be the n X n determinant with (i,j)-entry equal to 1 or 0 according as i + j is a cube or not. Then A(n) is nonzero for any n > 176.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..400
EXAMPLE
a(1) = 0 since 1 + 1 = 2 is not a square.
MATHEMATICA
SQ[n_]:=IntegerQ[Sqrt[n]]
a[n_]:=Det[Table[If[SQ[i+j]==True, 1, 0], {i, 1, n}, {j, 1, n}]]
Table[a[n], {n, 1, 30}]
PROG
(PARI) a(n)=matdet(matrix(n, n, i, j, issquare(i+j))) \\ Ralf Stephan, Sep 17 2013
CROSSREFS
KEYWORD
sign
AUTHOR
Zhi-Wei Sun, Aug 28 2013
STATUS
approved