# Is there some database or software to look for patterns in polynomials?

Like if I am looking at these polynomials,

$$x^8-8x^6+20x^4-16x^2+3$$

$$x^{10}-12x^8+48x^6-72x^4+33x^2$$

$$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$

And I want to know if they are members of some known sequence or not..

How can I go about it?

• there's always the Online Encyclopedia of Integer Sequences. Commented Feb 14, 2015 at 22:29
• But how does that help with polynomial sequences? Commented Feb 14, 2015 at 22:33
• This site might be able to help if you tell us where those polynomials come from/how to generate more. Three data points isn't exactly enough to fill the absence of meaning behind them. Commented Feb 14, 2015 at 22:35
• I am not sure that is easy to explain - these come from certain spectrum calculation on graphs - but its very off the standard things - the first one corresponds to K22, the next one is K23 and last one from K24 and so on... Commented Feb 14, 2015 at 22:36
• I'm fairly certain that the next polynomial starts with $x^{14}-20x^{12}$. The next term might or might not be $140x^{10}$. Commented Feb 15, 2015 at 1:22

Lots of super useful math tools. Try putting x^8−8x^6+20x^4−16x^2+3 vs x^10−12x^8+48x^6−72x^4+33x^2 in the prompt, for example.