11
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Recamán's sequence (A005132) is a mathematical sequence, defined as such:

$$A(n) = \begin{cases}0 & \textrm{if } n = 0 \\ A(n-1) - n & \textrm{if } A(n-1) - n \textrm{ is positive and not already in the sequence} \\ % Seems more readable than %A(n-1) - n & \textrm{if } A(n-1) > n \wedge \not\exists m < n: A(m) = A(n-1)-n \\ A(n-1) + n & \textrm{otherwise} \end{cases}$$

An alternative, simpler verbal explanation is as follows:

Subtract unless you can't (the number is negative, or has been used before), in which case add.

The first few terms are \$0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11\$

Now, there is already this challenge which asks you to generate the nth term of the sequence. This one is slightly different.

Challenge

Given a number n, draw the first n terms of the sequence. What do I mean by 'draw'? Let me demonstrate:

  1. Draw a number line max([A(y) for y<=n]) units long. We'll assume n is 5, for now, so the number line is 6 units long (since the largest of \$A(1) = 0\$, \$A(2) = 1\$, \$A(3) = 3\$, \$A(4) = 6\$ and \$A(5) = 2\$ is \$6\$). Make the line from underscores, starting at 0:

______

  1. Start with the transition between the first and second terms: that is, 0 and 1. Use | and - to draw a square (equal length and height), going upwards. In this case, we'll have to miss out the - because the distance is only 1.
||
______
  1. Now, we'll draw on the next step (\$A(2) = 1\$ to \$A(3) = 3\$) on the bottom of the line (we alternate between up and down each time):
||
______
 | |
 |-|

As you can see, this line also has a height of 2, since the height must be equal to the distance between the two terms.

If we continue, we will eventually get to:

   |--|
   |  |
|| |  |
______
 |||  |
 |||  |
  |   |
  |---|

Rules

  • If there is a - and | colliding, the later one takes priority.
  • There may be preceeding/trailing spaces before/after the image, but trailing/preceeding _s or -s are not allowed (exception is 0- or 1- indexing)
  • You can choose to set the 0 point just before the first _ on the number line, or just after it.
  • No alternative characters for -, | or _ may be used.
  • This is , so shortest answer in bytes wins.

Test case

Here is another test case, with n=10

            |-------|
            ||-----||
            ||     ||
  |----|    ||     ||
  |    |    ||     ||
  ||--||    ||     ||
  ||  ||    ||     ||
||||  ||    ||     ||
_____________________
 |||  ||   |||     ||
 |||  ||   |||     ||
  |   ||   |||     ||
  |---||   |||     ||
       |   |||     ||
       |---|||     ||
           ||------||
           |--------|
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  • \$\begingroup\$ It is not clear where left edge of square should be placed. \$\endgroup\$ – Daniil Tutubalin Jul 18 at 16:55
  • \$\begingroup\$ @DaniilTutubalin I'm not sure I understand what you mean. \$\endgroup\$ – Geza Kerecsenyi Jul 18 at 16:56
  • \$\begingroup\$ basically, statement only specifies that we need to draw squares (width = height) and that they should alternate between up and down. There are no instructions about squares' size and position. In test case I see that 2 squares may have the same position of left edge. \$\endgroup\$ – Daniil Tutubalin Jul 18 at 17:03
  • \$\begingroup\$ I think As you can see, this line also has a height of 2, since the height must be equal to the distance between the two terms., as well as You can choose to set the 0 point just before the first _ on the number line, or just after it. wrap this up pretty well. \$\endgroup\$ – Geza Kerecsenyi Jul 18 at 17:05
  • \$\begingroup\$ I think the test case for n=10 is wrong from 13-> 20 onwards. \$\endgroup\$ – Nick Kennedy Jul 18 at 21:41
4
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Jelly, 70 65 bytes

µ_ż+ɗLṪ>Ƈ-ḟ⁸Ḣṭµ¡µL;ⱮṀ’ṭr,;ɗƝJW,RN¹ƭƲ€$+Lp""ƲZẎ€Ʋ‘ŒṬ×"J$»/ị“-|_ ”Y

Try it online!

A full program taking a single integer \$n\$ via STDIN and outputting the ASCII art based on zero-indexing.

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