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

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

Printable View

- Sep 30th 2009, 07:40 AMvexikedInteresting 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 AMCaptainBlack
I'm not surprised, see this

CB - Sep 30th 2009, 08:11 AMTravisH82
- Sep 30th 2009, 08:38 AMpomp
Labelling $\displaystyle a_0, a_1, a_2, \ldots$ . Then $\displaystyle a_1$ is the first triangular number, $\displaystyle a_2$ is the second square number, $\displaystyle a_3$ 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: $\displaystyle a_n = n \left( {}^nC_2 + 1 \right)$ works.