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Triangle read by rows, a signed variant of A077049 * A128407; as infinite lower triangular matrices
3

%I #5 Mar 03 2013 13:39:38

%S 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 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 0,0,-1,1,1,0,0,-1,0,0

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

%C Row sums = mu(n), A008683

%F Given (-1)*triangle A077049, preface this with a "1" as row 1; = M.

%F Perform M * A128407 (the diagonalized variant of A008683); = A176918 as an

%F infinite lower triangular matrix.

%e First few rows of triangle A176918 =

%e 1;

%e -1, 0;

%e -1, 0, 0;

%e -1, 1, 0, 0;

%e -1, 0, 0, 0, 0;

%e -1, 1, 1, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0;

%e -1, 1, 0, 0, 0, 0, 0, 0;

%e -1, 0, 1, 0, 0, 0, 0, 0, 0;

%e -1, 1, 0, 0, 1, 0, 0, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

%e -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

%e -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;

%e -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 -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 ...

%Y Cf. A077049, A128407, A008683, A176890 (another version).

%K tabl,sign

%O 1,1

%A _Gary W. Adamson_ and _Mats Granvik_, Apr 29 2010