%I #2 Mar 30 2012 17:25:32
%S 1,1,1,1,0,2,1,1,0,3,1,0,0,0,5,1,1,2,0,0,6,1,0,0,0,0,0,10,1,1,0,3,0,0,
%T 0,11,1,0,2,0,0,0,0,0,16,1,1,0,0,5,0,0,0,0,19,1,0,0,0,0,0,0,0,0,0,26,
%U 1,1,2,3,0,6,0,0,0,0,0,27,1,0,0,0,0,0,0,0,0,0,0,0,40
%N Eigentriangle of A051731, the inverse Mobius transform.
%C Right border = A003238. Row sums = A003238 shifted one place to the left.
%C Sum of n-th row terms = rightmost term of next row. The sequence A003238: (1, 1, 2, 3, 5, 6, 10, 11,...) = the eigensequence of the inverse Mobius transform, A051731.
%C First few rows of the triangle =
%C 1;
%C 1, 1;
%C 1, 0, 2;
%C 1, 1, 0, 3;
%C 1, 0, 0, 0, 5;
%C 1, 1, 2, 0, 0, 6;
%C 1, 0, 0, 0, 0, 0, 10;
%C 1, 1, 0, 3, 0, 0, 0, 11;
%C 1, 0, 2, 0, 0, 0, 0, 0, 16;
%C 1, 1, 0, 0, 5, 0, 0, 0, 0, 19;
%C ...
%C n-th row = termwise product of A051731 terms and the first n terms of A003238: (1, 1, 2, 3, 5, 6, 10, 11,...). Example: row 6 = (1, 1, 2, 0, 0, 6) = termwise product of (1, 1, 1, 0, 0, 1) and (1, 1, 2, 3, 5, 6).
%F Triangle read by rows, A051731 * (A003238 * 0^(n-k)); 1<=k<=n
%Y A051731, Cf. A003238
%K nonn,tabl
%O 1,6
%A _Gary W. Adamson_, Sep 01 2008
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