Calculate a Subsequence
Calculator for finite subsequences. A subsequence is a part of a sequence, where some elements, derived from another sequence, are kept, others are deleted. The partition formula must be a strictly increasing sequence of positive integers. As running variable of the sequence, which is increased according to the partition formula in each step, j is used. The variable of the partition formula is k. Allowed input for the subsequence formula is similar to that of a sequence. For the partition formula, + - * and power are allowed.
Example: j=2*k-1 produces every odd number as input for the subsequence, pow(j#2) squares them. This subsequence is the default setting in this calculator. If you want even square numbers instead of odd square numbers, simply write 2*k instead of 2*k-1.
The output is displayed as a table with three rows. The first row contains the values for k, which are determined by the subsequence from km to kn. The default is 1 to 10. The second row contains the values for j, which are permitted by the partition formula. In this example, these are the odd numbers up to and including 19. The third row provides the results of the numbers from the partition rule inserted into the formula for the subsequence. Here, these are the squares of the odd numbers from 1 to 19. The last value is 19² = 361.
A subsequence that considers only even or odd terms has obviously a very simple division rule. This distinction is frequently made, as many mathematical processes and applications work with even or odd values. More complex partition rules are less common, but do also occur.
If you reverse the default setting, i.e., 2*j-1 for the subsequence formula and pow(k#2) for the partition formula, then you get double the values of the squares of the natural numbers minus one in the result row.
