cp's OEIS Frontend

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

%I A119530 #14 Jun 06 2023 14:01:22
%S A119530 1,-1,12,0,-409,0,4144,0,5040,0,142291,0,29139,0,0,0,0,0,-71577990,0,
%T A119530 3815616,0,-288128476,0,-248768000,0,0,0,-28714176,0,0,0,0,0,
%U A119530 -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 A119530 Determinant of n X n matrix of first n^2 odious numbers: odd number of 1's in binary expansion (A000069).
%e A119530 a(3) = 12 =
%e A119530   | 1  2  4|
%e A119530   | 7  8 11|
%e A119530   |13 14 16|.
%e A119530 a(4) = 0 because of the singular matrix 0 =
%e A119530   | 1  2  4  7|
%e A119530   | 8 11 13 14|
%e A119530   |16 19 21 22|
%e A119530   |25 26 28 31|.
%e A119530 a(6) = 0 because of the singular matrix whose lower right entry is 127.
%t A119530 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 A119530 (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 A119530 Cf. A000069, A119493.
%K A119530 sign
%O A119530 1,3
%A A119530 _Jonathan Vos Post_, May 27 2006
%E A119530 More terms from _Harvey P. Dale_, Jun 28 2012