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Alternating Sign Sequence

Introduction

The sign of a number is either a +, or a - for every non-zero integer. Zero itself is signless (+0 is the same as -0). In the following sequence, we are going to alternate between the positive sign, the zero and the negative sign. The sequence starts with 1, so we write 1 with a positive sign, with zero (this one is weird, but we just multiply the number by 0) and the negative sign:

1, 0, -1

The next number is 2, and we do the same thing again:

2, 0, -2

The sequence eventually is:

1, 0, -1, 2, 0, -2, 3, 0, -3, 4, 0, -4, 5, 0, -5, 6, 0, -6, 7, 0, -7, ...

Or a more readable form:

a(0) = 1
a(1) = 0
a(2) = -1
a(3) = 2
a(4) = 0
a(5) = -2
a(6) = 3
a(7) = 0
a(8) = -3
a(9) = 4
...

The Task

Given a non-negative integer n, output the n^th term of the above sequence. You can choose if you use the zero-indexed or one-indexed version.

Test cases:

Zero-indexed:

a(0) = 1
a(11) = -4
a(76) = 0
a(134) = -45
a(296) = -99

Or if you prefer one-indexed:

a(1) = 1
a(12) = -4
a(77) = 0
a(135) = -45
a(297) = -99

This is code-golf, so the submission with the smallest number of bytes wins!

Answer*

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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\$\begingroup\$ Hi and welcome to PPCG! Do you have a link I can test this (preferably online)? \$\endgroup\$

Riker
– Riker

2016年06月02日 02:54:09 +00:00
Commented Jun 2, 2016 at 2:54
\$\begingroup\$ @EᴀsᴛᴇʀʟʏIʀᴋ, thanks! Here's a link to an online applet thingamabob. The page looked blank for a little while, but then it showed up. \$\endgroup\$

juh
– juh

2016年06月02日 21:30:28 +00:00
Commented Jun 2, 2016 at 21:30
\$\begingroup\$ Oh cool. But how where do I put in the formula? >_> I tried pasting it into the blank, and it prompted to create a slider, but nothing else happened. \$\endgroup\$

Riker
– Riker

2016年06月02日 22:37:26 +00:00
Commented Jun 2, 2016 at 22:37
\$\begingroup\$ @EᴀsᴛᴇʀʟʏIʀᴋ: Over on the left-hand side, where it says "Input..." First, to initialise n, enter something like n=297 (this will give you a slider that's configured nicely). Then paste the formula into the Input box, which should now be below the n. (Make sure to hit return ;) The formula should evaluate to the nth term of the sequence, and it should change when you move the slider. \$\endgroup\$

juh
– juh

2016年06月02日 22:50:55 +00:00
Commented Jun 2, 2016 at 22:50

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