What is the logic in this number sequence?

Question

I’ve got a calendar with usually fairly simple logic or math puzzles, but was unable to solve this. You are allowed to use multiplication, sum, minus and division to calculate the next number.

The answer was 58, but there was no explaining formula, does anyone have a clue?

Update: an example of another sequence that was much easier to solve is this: 9 - 17 - 14 - 22 - 19 - ? Where the solution was simply alternating +8 and -3, so the answer here was 27.

Answer 1

Got the answer from the creators of the calendar:

(translated from Dutch)

The number sequence is 1, 4, 13, 31, 58. You get to this in the following way:

Between 1 and 4 is 3, between 4 and 13 is 9, between 13 en 31 is 18, between 31 and 58 27.

This related to the table of 3's in this way:

1 X 3 = 3
3 X 3 = 9
6 X 3 = 18
9 X 3 = 27

This how you get to the next number.

The first step being 1 x 3 really messes up the sequence in my opinion, but yeah I guess that is just the problem with arbitrary number sequences.

Answer 2

With $$a_n=1+\frac{n(n+1)(n-1)}2,$$ the next term would be 61 instead.

Seriously, number sequences are highly arbitrary. Who would guess that the next number after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59$ is $60$ - because it lists the orders of non-trivial simple groups?