%I #7 May 01 2013 04:06:35
%S 1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,0,
%T 0,1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,
%U 0,1,0,0,0,1,0,0,0,0
%N Triangle read by rows, A047999 * A010060 (diagonalized); as infinite lower triangular matrices.
%C Row sums = A048896: (1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4,...). Right border = Thue-Morse sequence A010060, starting with offset 1.
%F Let S = Sierpinski's gasket, A047999. Let Q = a diagonalized version of the Thue-Morse sequence, A010060: [0; 0,1; 0,0,1; 0,0,0,0; 0,0,0,0,1;...], (i.e. A010060 as the rightmost diagonal and the rest zeros). A167364 = S * Q, as infinite lower triangular matrices. Delete leftmost column of zeros.
%e First few rows of the triangle =
%e 1;
%e 0, 1;
%e 1, 1, 0;
%e 0, 0, 0, 1;
%e 1, 0, 0, 1, 0;
%e 0, 1, 0, 1, 0, 0;
%e 1, 1, 0, 1, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 1;
%e 1, 0, 0, 0, 0, 0, 0, 1, 0;
%e 0, 1, 0, 0, 0, 0, 0, 1, 0, 0;
%e 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1;
%e 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0
%e 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1;
%e 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1;
%e 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0;
%e 0, 0, 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, 0;
%e 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0;
%e 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1;
%e ...
%Y Cf. A047999, A010060.
%K nonn,tabl
%O 1,1
%A _Gary W. Adamson_ & _Mats Granvik_, Nov 01 2009
|