|
%I #15 Apr 02 2019 05:42:25
%S 1,-1,1,-1,-1,1,0,-1,-1,1,-1,0,-1,-1,1,1,-1,0,-1,-1,1,-1,1,-1,0,-1,-1,
%T 1,0,-1,1,-1,0,-1,-1,1,0,0,-1,1,-1,0,-1,-1,1,1,0,0,-1,1,-1,0,-1,-1,1,
%U -1,1,0,0,-1,1,-1,0,-1,-1,1
%N Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) "decrescendo".
%H E. Deutsch, L. Ferrari and S. Rinaldi, <a href="https://doi.org/10.1016/j.aam.2004.05.002">Production Matrices</a>, Advances in Applied Mathematics, 34 (2005) pp. 101-122.
%F Triangle read by rows, T(n,k) = A008683(n-k+1) = A008683 in every column = A008683 "decrescendo"d by rows.
%e Triangle begins
%e 1;
%e -1, 1;
%e -1, -1, 1;
%e 0, -1, -1, 1;
%e -1, 0, -1, -1, 1;
%e 1, -1, 0, -1, -1, 1;
%e -1, 1, -1, 0, -1, -1, 1;
%e 0, -1, 1, -1, 0, -1, -1, 1;
%e 0, 0, -1, 1, -1, 0, -1, -1, 1;
%e ...
%e Production matrix begins
%e -1, 1,
%e -2, 0, 1,
%e -3, 0, 0, 1,
%e -6, 0, 0, 0, 1,
%e -9, 0, 0, 0, 0, 1,
%e -17, 0, 0, 0, 0, 0, 1,
%e -28, 0, 0, 0, 0, 0, 0, 1,
%e -50, 0, 0, 0, 0, 0, 0, 0, 1,
%e -83, 0, 0, 0, 0, 0, 0, 0, 0, 1,
%e -147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ...
%e where first column is -A073776(n+1). - _Paul Barry_, Feb 10 2011
%Y Cf. A008683, A002321, A073776, A152901, A152902.
%Y Row sums = A002321, the Mertens function. A185694 is an eigensequence.
%K tabl,sign
%O 1,1
%A _Gary W. Adamson_, Dec 14 2008
|
