find the expression in terms of n of the nth term of following squences

Question

5,13,32,69,129,221....help plz show it work

Answer 1

I looked at that yesterday, but I could not find an obvious pattern

Found this:
5 = 2^2 + 1^2
13 = 3^2 + 2^2
but then it broke apart on the next one

Took differences and got:

5
13 -- 8
32 -- 19 -- 11
69 -- 37 -- 18 -- 7
129 - 60 -- 23 -- 5 -- 2
221 - 92 -- 32 -- 9 -- 4

not enough terms to tell if the 5th difference column is linear.
If the 6th column turns out to be a constant , then you would have a 6th degree polynomial

sorry, can't find out more at this time

Answer 2

I suspect a typo.
6 = 1^3+5
13 = 2^3+5
32 = 3^3+5
69 = 4^3+5
130 = 5^3+5
221 = 6^3+5

If no typos, then I'm stuck, too.