%I A136562
%S A136562 1,3,9,14,26,36
%N A136562 Consider the triangle A136561: the 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 A136562 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.) The rightmost diagonal of the Zorach additive 
               triangle is A035313.
%H A136562 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A136562 The triangle begins:
%e A136562 1,
%e A136562 2,3,
%e A136562 4,6,9,
%e A136562 -5,-1,5,14,
%e A136562 13,8,7,12,26,
%e A136562 -30,-17,-9,-2,10,36.
%e A136562 Example:
%e A136562 Considering the right-most value of the 4th row: Writing a 10 here instead, 
               the first 4 rows of the triangle become:
%e A136562 1
%e A136562 2,3
%e A136562 4,6,9
%e A136562 -9,-5,1,10
%e A136562 But 1 already occurs earlier in the triangle. So 10 is not the right-most 
               element of row 4.
%e A136562 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. So A136562(4) = 13.
%Y A136562 Cf. A035313, A136561, A136563.
%Y A136562 Sequence in context: A103813 A001968 A111907 this_sequence A100785 A056287 
               A050005
%Y A136562 Adjacent sequences: A136559 A136560 A136561 this_sequence A136563 A136564 
               A136565
%K A136562 more,nonn
%O A136562 1,2
%A A136562 Leroy Quet Jan 06 2008