Discover the Secret Formula for Relating N and t in this Number Pattern

[orthovector]

anybody know how I can relate N with t?


when N=1 t=0, N=2 t=1, N=3 t=3, N=4 t=6, N=5 t=10, N=6 t=15, N=7 t=21...and so on.

i need to derived a formula that relates N to t.

HELP!

 

[Mark44]

Each increment in t jumps by one more than the preceding increment. The t-sequence is {0, 1, 3, 6, 10, 15, 21, ...}

There's a way to solve this using difference equations (which are something like differential equations, but not the same). In this problem the first differences are 1, 2, 3, 4, and so on, and the second differences are all 1.

The technique escapes me at the moment, and I'm heading off to bed. In the meantime, you might try a search for "difference equations" and see if that helps you.

 

[Dadface]

Start by tabulating values of N and N squared.

 

[orthovector]

Each increment in t jumps by one more than the preceding increment. The t-sequence is {0, 1, 3, 6, 10, 15, 21, ...}

There's a way to solve this using difference equations (which are something like differential equations, but not the same). In this problem the first differences are 1, 2, 3, 4, and so on, and the second differences are all 1.

The technique escapes me at the moment, and I'm heading off to bed. In the meantime, you might try a search for "difference equations" and see if that helps you.

thanks mark, I'll try to work on it a bit more...I think these number patterns are very interesting...

 

[orthovector]

help!

 

[Mark44]

This is actually a bit simpler than I first thought. Here are the numbers you gave, plus a few more, assuming they follow the same pattern

N |1|2|3|4| 5| 6| 7| 8| 9|
---------------------------
t |0|1|3|6|10|15|21|28|37|

First, I'd like to get rid of t, and switch to a_N, since I would like to be able to identify which value in the second row I'm talking about. The bottom row has values of a_i, where i >= 1. I stared at the table for a while, then noticed this pattern:
a₁ = 0
a₂ = a₁ + 1
a₃ = a₂ + 2
a₄ = a₃ + 3
.
.
.
a_N = ? + ?

That should get you started.