# What number continues the sequence?

What number continues the sequence?

1 2 4 8 16 31 ?

Hint:

The numbers are the answers of a mathematical question.

• – Mithrandir Oct 25 '17 at 14:23

The next number is

57

Because these are the

Maximal number of regions obtained by joining n points around a circle by straight lines

57: the number of regions a circle is divided into by $n$ points.

or

61: the "Pentanacci" numbers, where each number is generated from adding the previous five (and numbers before the start of the sequence are 0).

or perhaps

62: the divisors of 492, the third perfect number.

or even

46: the Stoehr sequence for $h=4$.

or maybe

60: the number of binary sequences of length $n$ not containing "01110".

All of these were found with the OEIS, and they all give different answers. I assume you're looking for the first one, but the second is plausible as well.

• the second one is not a mathematical question. It is a number sequence. – yukashima huksay Oct 30 '17 at 14:47
• I don't thing my sequence was a nice sequence anyway tho:D – yukashima huksay Oct 30 '17 at 14:47

These are

(maximal) numbers of regions formed by placing 1,2,... points on the circumference of a circle and joining them with straight lines. This equals $\binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\binom{n}{3}+\binom{n}{4}$, which is the same as $2^n$ for $n\leq4$, but after that grows more slowly.

[EDITED because I'd slightly fluffed the description.]