

A228624


Determinant of the n X n matrix with (i,j)entry equal to 1 or 0 according as i + j is a square or not.


2



0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 2, 3, 3, 1, 0, 1, 1, 2, 5, 13, 7, 7, 6, 1, 8, 1, 17, 25, 13, 12, 11, 12, 11, 12, 4, 1, 1, 66, 60, 26, 13, 40, 67, 1, 82, 81, 49, 32, 68, 103, 222, 503, 39, 134
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OFFSET

1,17


COMMENTS

Conjecture: a(n) is nonzero for any n > 21.
ZhiWei 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



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



STATUS

approved



