data/problems/155.yml
---
:id: 155
:name: Counting Capacitor Circuits
:url: https://projecteuler.net/problem=155
:content: "An electric circuit uses exclusively identical capacitors of the same value
C. \nThe capacitors can be connected in series or in parallel to form sub-units,
which can then be connected in series or in parallel with other capacitors or other
sub-units to form larger sub-units, and so on up to a final circuit.\n\nUsing this
simple procedure and up to <var>n</var> identical capacitors, we can make circuits
having a range of different total capacitances. For example, using up to <var>n</var>=3
capacitors of 60 F each, we can obtain the
following 7 distinct total capacitance values:\n\n \n\nIf
we denote by <var>D</var>(<var>n</var>) the number of distinct total capacitance
values we can obtain when using up to <var>n</var> equal-valued capacitors and the
simple procedure described above, we have: <var>D</var>(1)=1, <var>D</var>(2)=3,
<var>D</var>(3)=7 ...\n\nFind <var>D</var>(18).\n\n_Reminder :_ When connecting
capacitors C<sub>1</sub>, C<sub>2</sub> etc in parallel, the total capacitance is
C<sub>T</sub> = C<sub>1</sub> + C<sub>2</sub> +..., \nwhereas
when connecting them in series, the overall capacitance is given by: \n\n"