%I A136561
%S A136561 1,2,3,4,6,9,5,1,5,14,13,8,7,12,26,30,17,9,2,10,36
%V A136561 1,2,3,4,6,9,-5,-1,5,14,13,8,7,12,26,-30,-17,-9,-2,10,36
%N A136561 Triangle read by rows: n-th diagonal (from the right) is the sequence 
               of (signed) differences between pairs of consecutive terms in the 
               (n-1)th diagonal. The right-most diagonal (A136562) is defined: A136562(1)=1; 
               A136562(n) is the smallest integer > A136562(n-1) such that any (signed) 
               integer occurs at most once in the triangle A136561.
%C A136561 Requiring that the absolute values of the differences in the difference 
               triangle only occur at most once each leads to the Zorach additive 
               triangle. (See A035312.)
%H A136561 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A136561 The triangle begins:
%e A136561 1,
%e A136561 2,3,
%e A136561 4,6,9,
%e A136561 -5,-1,5,14,
%e A136561 13,8,7,12,26,
%e A136561 -30,-17,-9,-2,10,36.
%e A136561 Example:
%e A136561 Considering the right-most value of the 4th row: Writing a 10 here instead, 
               the first 4 rows of the triangle become:
%e A136561 1
%e A136561 2,3
%e A136561 4,6,9
%e A136561 -9,-5,1,10
%e A136561 But 1 already occurs earlier in the triangle. So 10 is not the right-most 
               element of row 4.
%e A136561 Checking 11,12,13,14; 14 is the smallest value that can be the right-most 
               element of row 4 and not have any elements of row 4 occur earlier 
               in the triangle.
%Y A136561 Cf. A035312, A136562, A136563.
%Y A136561 Sequence in context: A105808 A124058 A118080 this_sequence A112868 A111792 
               A113197
%Y A136561 Adjacent sequences: A136558 A136559 A136560 this_sequence A136562 A136563 
               A136564
%K A136561 more,sign,tabl
%O A136561 1,2
%A A136561 Leroy Quet Jan 06 2008