Find closed form of a sequence $2,5,11,23,...$ Find closed form of a sequence $2,5,11,23,\dots$
How to get generating function for this sequence (closed form)?
Explicit form is $f(x)=2+5x+11x^2+23x^3+\cdots$
Is it possible to get to geometric series representation?
I tried to derive the series multiple times, but that doesn't help.
Could someone give a hint?

$2, 5, 11, 23, 47, \cdots$ Well, I think $a_n = 3 \cdot 2^{n - 1} - 1$ here.
OK, let me elaborate a bit. Observe that $d_n := a_{n + 1} - a_{n} = 3 \cdot 2^{n - 1}$. Since $$a_n - a_1 = \sum_{k = 1}^{n - 1} d_{k} = 3 \sum_{k = 1}^{n - 1} 2^{k - 1} = 3 \cdot (2^{n - 1} - 1) = 3 \cdot 2^{n - 1} - 3.$$ Since $a_1 = 2$, we have $a_n = 3 \cdot 2^{n - 1} - 1$.
