[seqfan] Triangles of sums

[jnthn stdhr]

Hello seqfans.

Long time no sequence (apologies.)  Inspired by , http://oeis.org/A340389
wondered if a generalized sequence, the number of sum triangles of n,  was
in the database -- it appears it is not.

If we define a sum triangle of n as a triangle with n at its apex, all
pair-wise members (x, y) of rows 2,3,4,... sum to the element immediately
above, every element is distinct, and rows are complete (length of row m =
length of row (m-1) + 1.

For example:

          8         9        9
 3      6 4      6 3     6 3
2 1   5 1 3   5 1 2  4 2 1


The sequence I get for n=1 to 30 is:


[1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 9, 11, 11, 18, 17, 22, 23, 29, 31, 38,
37, 46, 49, 58, 59, 72, 76, 86, 90]

My python code is about 70 lines long.  Maybe a MMA expert could write a
more concise program and confirm the the sequence?

-Jonathan