# Interesting sequence - find closed form

• Sep 30th 2009, 07:40 AM
vexiked
Interesting sequence - find closed form
This sequence has me stumped.... anyone have an idea on what the closed form is?

0, 1, 4, 12, 28, 55, 96, 154
• Sep 30th 2009, 08:00 AM
CaptainBlack
Quote:

Originally Posted by vexiked
This sequence has me stumped.... anyone have an idea on what the closed form is?

0, 1, 4, 12, 28, 55, 96, 154

I'm not surprised, see this

CB
• Sep 30th 2009, 08:11 AM
TravisH82
Quote:

Originally Posted by CaptainBlack
I'm not surprised, see this

CB

Whoa! awesome resource. CaptainBlack, can you point me to a sticky with useful links such as that? I've been searching around with the google, but come up with too much random junk.

Thanks!
• Sep 30th 2009, 08:38 AM
pomp
Quote:

Originally Posted by vexiked
This sequence has me stumped.... anyone have an idea on what the closed form is?

0, 1, 4, 12, 28, 55, 96, 154

Labelling $a_0, a_1, a_2, \ldots$ . Then $a_1$ is the first triangular number, $a_2$ is the second square number, $a_3$ is the third pentagonal number, etc...

I'm just working on a closed form but it shouldn't be too difficult at all.

Pomp

EDIT: $a_n = n \left( {}^nC_2 + 1 \right)$ works.