Question 1097251
<pre>
Start with 3
Double 3, get 6, add +1, get 7.
Double 7, get 14, add 0, get 14.
Double 14, get 28, add -1 get 27.
Double 27, get 54, add -2, get 52.
Double 52, get 104, add -3, get 101.
Double 101, get 202, add -4, get 198.
Double 198, get 396, add -5, get 391.
Double 391, get 782, add -6, get 776.
Double 776, get 1552, add -7, get 1545.
Double 1545, get 3090, add -8, get 3082.
Double 3082, get 6164, add -9, get 6155.
Double 6155, get 12310, add -10, get 12300.
Double 12300, get 24600, add -11, get 24589.
Double 24589, get 49178, add -12, get 49166.
Double 49166, get 98332, add -13, get 98319.
Double 98319, get 196638, add -14, get 196624.
Double 196624, get 393248, add -15, get 393233.
Double 393233, get 786466, add -16, get 786450.
Double 786450, get 1572900, add -17, get 1572883.
Double 1572883, get 3145766, add -18, get 3145748.
Double 3145748, get 6291496, add -19, get 6291477.
Double 6291477, get 12582954, add -20, get 12582934.
Double 12582934, get 25165868, add -21, get 25165847.

Here's that recursion formula:

{{{a[1]}}}{{{""=""}}}{{{3}}},    {{{a[n+1]}}}{{{""=""}}}{{{2a[n]-n+3}}}

Here's another recursion formula for the same sequence:

{{{a[1]}}}{{{""=""}}}{{{3}}},    {{{a[n+1]}}}{{{""=""}}}{{{a[n]+3*2^(n-2)+1}}}

Did you want a general formula?

Edwin</pre>