Interesting sequence - find closed form

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September 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
September 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
September 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!
September 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.

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