What comes next?

6
16
1116
3116
?

132116

1113122116

311311222116

13211321322116

The next term is pretty clearly 7.

:dubious: How?

Just start plugging natural numbers into the expression

(-5819n^4 + 57430n^3 - 186025n^2 + 243590n - 109032)/24.

You get 6, 16, 1116, 3116, 7, -20039, etc.

Pretty obvious, really.

Hoopy Frood is correct.

So are the people who came after me, since they continued the sequence.

And Lubricious Integument is right as well. (Thank you google calculator.)

Yes, everyone’s correct but I think Lubricious Integument wins the thread.

I just want to know how long that took him (her?) and what method he used to figure that out. Because I can’t see anyone bothering to figure that out by hand.

Yup 132116.

How about…

What’s the next line:

1
1 7
1 7 6
1 7 6 3
5 1 7 6 3
5 9 1 7 6 3
5 9 1 7 6 3 0
5 9 1 7 6 3 2 0
5 4 9 1 7 6 3 2 0

I don’t know the technique, but I’m guessing it was slightly tongue-in-cheek, making the point that these types of numerical sequence puzzles inherently have many solutions. An infinite number of solutions, I imagine.

You can always learn something here in dope!:cool:

http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
I used to give problems on this to my beginning algebra class… didn’t go well.