A119530 Determinant of n X n matrix of first n^2 odious numbers: odd number of 1's in binary expansion (A000069).

1, -1, 12, 0, -409, 0, 4144, 0, 5040, 0, 142291, 0, 29139, 0, 0, 0, 0, 0, -71577990, 0, 3815616, 0, -288128476, 0, -248768000, 0, 0, 0, -28714176, 0, 0, 0, 0, 0, -6040500480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -795328048345114368

Offset: 1

Author

Jonathan Vos Post, May 27 2006

Keywords

• sign

Examples

			a(3) = 12 =
  | 1  2  4|
  | 7  8 11|
  |13 14 16|.
a(4) = 0 because of the singular matrix 0 =
  | 1  2  4  7|
  | 8 11 13 14|
  |16 19 21 22|
  |25 26 28 31|.
a(6) = 0 because of the singular matrix whose lower right entry is 127.
		

Crossrefs

Cf. A000069, A119493.

Programs

Mathematica

nn=10000;With[{xa=Select[Range[nn],OddQ[DigitCount[#,2,1]]&]},Table[Det[ Partition[Take[xa,n^2],n]],{n,Floor[Sqrt[Length[xa]]]}]] (* Harvey P. Dale, Jun 28 2012 *)

PARI

a(n)=matdet(matrix(n,n,i,j,k=(i-1)*n+j;2*k-1-hammingweight(k-1)%2)) \\ Charles R Greathouse IV, Mar 29 2013

Extensions

More terms from Harvey P. Dale, Jun 28 2012