Energy levels of electrons

Question

Energy levels of electrons

Electrons are ordered into "shells". However, sometimes electrons get excited, for example by heat, and leave their shell to go to another! These electrons will go back at some point, but they cannot go back to their original shell without emitting energy in the form of radio waves.

For example, the energy levels for hydrogen look like this:

The base energy level of an electron in hydrogen is at n = 1. If it gets 'excited', it might go to n = 4. However, on the way back, the electron does not always simply go from n = 4 to n = 1, it has different options. See the example.

Task

Write a program or function that takes an integer and outputs the amount of options the electron has to get back to its un-excited state. For this task, you can take granted that an electron can only emit energy from its excited state. It will not get more energy once it has been excited.

This is code-golf, the answer with the least amount of bytes wins.

If you are interested in these type of questions, check out this similar question. Also check out this for more info on these matters.

Input

The input of your function/program is a whole integer. It is greater than 0 and less than 2^31.

Output

An integer, the amount of options the electron has to return to its original state, which is n = 1 (for hydrogen). When the input is 1, return 0, as it is already in its original energy level.

Examples

Input: 4
Output: 4

Because the options are:

4 -> 3 -> 2 -> 1
4 -> 3 -> 1
4 -> 2 -> 1
4 -> 1

Visualised:

Answer 1

Pyth, 5 bytes

/^2Q4

I integer-divide by 4 instead of subtracting two from the power and flooring.

Answer 2

CJam, 6 8 7 bytes

1li2-m<

Try it online

Unless I completely misunderstood the question, the result is simply 2^(n-2). For each level between n and 1, you can either skip or not skip it on the way back.

Using the left shift operator instead of the power operator is one byte more, but gives the specified result 0 for n=1, while the power operator gives 0.5 for that case.

Explanation:

1     Push 1 for later shift operator.
li    Get input and convert to int.
2-    Subtract 2.
m<    Left-shift 1 by (n-2).

If I shamelessly stole Thomas Kwa's approach, this would be 6 bytes in CJam:

2li#4/

Answer 3

Dyalog APL, 6 bytes

⌊2*-∘2

This is a monadic function train. It is equivalent to the following, trainless function.

{⌊2*⍵-2}

Try it online on TryAPL.

How it works

   -∘2  Take the right argument and subtract 2.
 2*     Elevate 2 to the difference.
⌊       Round down to the nearest integer.

Answer 4

JavaScript ES7, 12 11 bytes

i=>2**(i-2)

Defines an anonymous function.

Answer 5

Python, 29 22 16 bytes

lambda n:2**n//4

Technique shamelessly stolen from Thomas's answer. Try it online

Answer 6

Stuck, 6 bytes

2i2-^)

Hey look I almost outgolfed Pyth outgolfed CJam

Answer 7

dc, 6

2?^4/p

Algorithm expertly lifted from other correct answers.

Testcases:

$ for t in 1 4; do dc -e'2?^4/p' <<< $t; done
0
4
$ 

Answer 8

Julia, 9 bytes

n->2^n÷4

Like several other answers, this uses Thomas's approach. ÷ performs integer division in Julia (but unfortunately is 2 bytes in UTF-8).

Answer 9

PHP, 28 bytes

I hope I got it right. floor handles the case for 1 where it should output 0

<?=floor(pow(2,$argv[1]-2));

Works from command line like:

electrons.php 4

_{+1 and thanks to Reto Koradi for providing the formula. ;)}

Answer 10

Minkolang 0.9, 7 bytes

Copying Thomas like everyone else...

2n;4:N.

This is a full program, and the first five characters are equivalent to 2**n//4 in Python 3. Try it online.