Getting equation from non-arithmetic and non-geometric sequences

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Before I go into my question, I have checked out Non arithmetic, non geometric series starting with 4 and 8., however I still cannot find a way to solve one.

Currently, lets start with the equation: $3n + 2^n$

The sequence will look like this: $5, 10, 17, 28, 47$

I've tried several ways like looking at the differences of the numbers, however $+5, +7, +11, +19$ doesn't give all that much detail. Sure there is $3 + 2^n$, but that is only for the difference. I can't find any relevance between that and the regular sequence.

I've tried other equations like $2n + 3^n$, and $2n + 2^n$, but to no avail.