%I A130093
%S A130093 1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,
%T A130093 1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0
%N A130093 A051731 * a lower triangular matrix with A036987 on the main diagonal 
               and the rest zeros.
%C A130093 Right border = A036987, the Fredholm-Rueppel sequence, (1, 1, 0, 1, 0, 
               0, 0, 1, 0,...). Row sums = the ruler function, A001511: (1, 2, 1, 
               3, 1, 2, 1, 4,...).
%C A130093 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 21 2009: 
               (Start)
%C A130093 A130093 also = A047999 (Sierpinski's gasket) * A036987 diagonalized, 
               as
%C A130093 infinite lower triangular matrices.
%C A130093 Eigensequence of A130093 = A001511, (same sequence as row sums). (End)
%C A130093 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2009: 
               (Start)
%C A130093 Equals Sierpinski's gasket, A047999 * A036987 (diagonalized); as infinite
%C A130093 lower triangular matrices. (End)
%F A130093 Inverse Moebius transform of a lower triangular matrix with A036987 (the 
               Fredholm-Rueppel sequence) on the main diagonal and the rest zeros.
%e A130093 First few rows of the triangle are:
%e A130093 1;
%e A130093 1, 1;
%e A130093 1, 0, 0;
%e A130093 1, 1, 0, 1;
%e A130093 1, 0, 0, 0, 0;
%e A130093 1, 1, 0, 0, 0, 0;
%e A130093 1, 0, 0, 0, 0, 0, 0;
%e A130093 1, 1, 0, 1, 0, 0, 0, 1;
%e A130093 ...
%Y A130093 Cf. A001511, A051731, A036987.
%Y A130093 Cf. A047999 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 21 2009]
%Y A130093 Cf. A047999 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2009]
%Y A130093 Sequence in context: A131078 A130657 A084846 this_sequence A166446 A103368 
               A055132
%Y A130093 Adjacent sequences: A130090 A130091 A130092 this_sequence A130094 A130095 
               A130096
%K A130093 nonn,tabl
%O A130093 1,1
%A A130093 Gary W. Adamson (qntmpkt(AT)yahoo.com), May 06 2007