[seqfan] Re: Triangles of sums

[Allan Wechsler]

I applaud your instinct to make sure that simple cases accompany their more
complicated brethren into the Encyclopedia -- I think this is right on
target.

But I am missing something here. Can you display all the triangles for n=1
to 3? My problem is that you must be allowing triangles of one row in order
to have one example for n=1 and n=2, but then it seems to me that you ought
to have two examples for n=3, one with one row, and one with two rows. But
you say there is only one.

Also, I am assuming you do *not* consider reflections around the vertical
axis to be distinct solutions.

I'm sure some sequence fanatic will be happy to help you as soon as it's
clearer what your definitions are.

One last thing: 6 + 4 does not equal 8, as your second example seems to
claim.

On Thu, Jul 22, 2021 at 5:06 PM jnthn stdhr <jstdhr at gmail.com> wrote:

> 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
>
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