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%I #14 Jun 06 2023 14:01:22
%S 1,-1,12,0,-409,0,4144,0,5040,0,142291,0,29139,0,0,0,0,0,-71577990,0,
%T 3815616,0,-288128476,0,-248768000,0,0,0,-28714176,0,0,0,0,0,
%U -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
%N Determinant of n X n matrix of first n^2 odious numbers: odd number of 1's in binary expansion (A000069).
%e a(3) = 12 =
%e | 1 2 4|
%e | 7 8 11|
%e |13 14 16|.
%e a(4) = 0 because of the singular matrix 0 =
%e | 1 2 4 7|
%e | 8 11 13 14|
%e |16 19 21 22|
%e |25 26 28 31|.
%e a(6) = 0 because of the singular matrix whose lower right entry is 127.
%t 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 *)
%o (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
%Y Cf. A000069, A119493.
%K sign
%O 1,3
%A _Jonathan Vos Post_, May 27 2006
%E More terms from _Harvey P. Dale_, Jun 28 2012
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