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%I #8 Jun 03 2023 06:33:28
%S 1,1,1,1,0,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,
%T 0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,
%U 0,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1
%N Gray code/ Silvester-Hadamard binary triangular sequence from 16 X 16 self-similar matrix.
%C See A140820 for another version.
%F a(n,m) = Antidiagonal[HadamardMatrix[n,m]]
%e {1},
%e {1, 1},
%e {1, 0, 1},
%e {1, 0, 0, 1},
%e {1, 1, 0, 1, 1},
%e {1, 1, 0, 0, 1, 1},
%e {1, 0, 0, 0, 0, 0, 1},
%e {1, 0, 0, 0, 0, 0, 0, 1},
%e {1, 1, 0, 0, 0, 0, 0, 1, 1},
%e {1, 1, 1, 1, 0, 0, 1, 1, 1, 1},
%e {1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1},
%e {1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1},
%e {1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1},
%e {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
%e {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
%e {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}
%t c[i_,k_]:=Floor[Mod[i/2^k,2]];
%t b[i_,k_]=If[c[i,k]==0&&c[i,k+1]\[Equal]0,0,If[c[ i,k]==1&&c[i,k+1]\[Equal]1,0,1]];
%t a0=Table[If[Sum[b[i,k]*b[j,k],{k,0,n}]\[Equal]0,1,0],{j,0,n},{i,0,n}];
%t ListDensityPlot[a0,Mesh\[Rule]False];
%t c=Delete[Table[Reverse[Table[a0[[n,l-n]],{n,1,l-1}]],{l,1,Dimensions[a0][[1]]+1}],1];
%t Flatten[c]
%Y Cf. A121801, A122944, A123949, A140820.
%K nonn,uned,tabl,obsc
%O 1,1
%A _Roger L. Bagula_, Sep 27 2007
%E This looks interesting, but I do not understand the definition. - _N. J. A. Sloane_, Oct 16 2008
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