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A176918 Triangle read by rows, a signed variant of A077049 * A128407; as infinite lower triangular matrices.

%I A176918 #7 Jul 22 2025 07:59:56
%S A176918 1,-1,0,-1,0,0,-1,1,0,0,-1,0,0,0,0,-1,1,1,0,0,0,-1,0,0,0,0,0,0,-1,1,0,
%T A176918 0,0,0,0,0,-1,0,1,0,0,0,0,0,0,-1,1,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,
%U A176918 0,0,-1,1,1,0,0,-1,0,0
%N A176918 Triangle read by rows, a signed variant of A077049 * A128407; as infinite lower triangular matrices.
%C A176918 Row sums = mu(n), A008683
%F A176918 Given (-1)*triangle A077049, preface this with a "1" as row 1; = M.
%F A176918 Perform M * A128407 (the diagonalized variant of A008683); = A176918 as an
%F A176918 infinite lower triangular matrix.
%e A176918 First few rows of triangle A176918 =
%e A176918 1;
%e A176918 -1, 0;
%e A176918 -1, 0, 0;
%e A176918 -1, 1, 0, 0;
%e A176918 -1, 0, 0, 0, 0;
%e A176918 -1, 1, 1, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 1, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 0, 0, 1, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
%e A176918 -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
%e A176918 -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A176918 ...
%Y A176918 Cf. A077049, A128407, A008683, A176890 (another version).
%K A176918 tabl,sign
%O A176918 1,1
%A A176918 _Gary W. Adamson_ and _Mats Granvik_, Apr 29 2010