1,2

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.

Leroy Quet, Home Page (listed in lieu of email address)

The triangle begins:

1,

2,3,

4,6,9,

-5,-1,5,14,

13,8,7,12,26,

-30,-17,-9,-2,10,36.

Example:

Considering the right-most value of the 4th row: Writing a 10 here instead, the first 4 rows of the triangle become:

1

2,3

4,6,9

-9,-5,1,10

But 1 already occurs earlier in the triangle. So 10 is not the right-most element of row 4.

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.

Cf. A035313, A136561, A136563.

Sequence in context: A103813 A001968 A111907 this_sequence A100785 A056287 A050005

Adjacent sequences: A136559 A136560 A136561 this_sequence A136563 A136564 A136565

more,nonn

Leroy Quet Jan 06 2008