About Up and Down:
This sequence, first described by Henry Bottomley, has a structure which closely relates to the succession of perfect squares (i.e. 4, 9, 16, 25, 36, etc.). Here is how the sequence begins: 0, 0, 0, 1, 0, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 3, 0, -3, -2, -1, 0, 1, 2, 3, 4, 0, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 0, -5, -4, -3, -2, -1, 0
To compute the nth term, simply take its square root. The nth term is equal to n - floor(sqrt(n)) * ceil(sqrt(n)). So for a perfect square, such as 25, this value is always 0. As another example, consider 8; its value is 8 - 2 * 3 = 2. (For the first term in the sequence, n = 0.)
For the most interesting results, go to the Mix tab and check the option for reverse play when integers are negative.
My name for this mode refers to a famous monologue by Puck in Shakespeare's A Midsummer Night's Dream.
To switch the musical structure to this mode, click on the Change button.
Reference: N. J. A. Sloane, editor (2002), The On-Line Encyclopedia of Integer Sequences, published electronically at http://www.research.att.com/~njas/sequences. Sequence A038760.