Question

Can you help me with this patten?
its a triangle like this:
1 1
3 2 3
6 4 4 6
10 7 6 7 10
15 11 9 9 11 15
and its supposed to be a triangle, like pascal's or something.
I need to find a general statement for the (r+1)th element in the nth row.

Answer 1

So is the top line 1 1 ? And no line above that?

Answer 2

yeah its just 1 1.

Answer 3

if you can find a pattern without the 1s though, i can probably manipulate it

Answer 4

\[\frac{n(n+1)}{2}-r(n-r)\quad ,\quad r=0,\dots,n\]

Answer 5

i know it says youre a lifesaver, but you really are a lifesaver. :) how did you find it?

Answer 6

Are you familiar with triangular numbers? It was presumably something based on them (see first element in each row), and it was just a question of finding what that variant was. Admittedly, I didn't do it, but I grew out of these type of problems a while ago.

Answer 7

okay thank you. i just need to know because it was like an investigation for a precalc class where we need to find it and then explain how we found it. i actually got the first part on my own but i was having a hard time with the r(n-r) part.

Answer 8

Well the (r-n) part kind of suggests itself because the last term is always equal to the first, but after that, yeah, just guesswork (as far as I can tell)

Answer 9

you mean the (n-r)?

Answer 10

Yes, that, unless you called it + r(r-n)

Answer 11

yeah. thank you so much, i was mad my teacher gave this to us and made us figure it out by ourselves. you saved my life.

Answer 12

Haha, hardly (I didn't work it out) - but if you weren't getting me confused with the person who posted it and found my ramblings useful, then thanks! :)

Answer 13

well your ramblings were useful. both of you were.

Answer 14

^_^