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

1,3

Links

Table of n, a(n) for n=1..61.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000069, A119493.

Sequence in context: A376441 A077351 A370018 * A012332 A012455 A120954

Adjacent sequences: A119527 A119528 A119529 * A119531 A119532 A119533

Keyword

sign

Author

Jonathan Vos Post, May 27 2006

Extensions

More terms from Harvey P. Dale, Jun 28 2012

Status

approved