Common Ascent

Math test

by Rosencrantz (Math)
Let's put the vBcode parser to work...

This sequence is similar to the Fibonacci sequence. It is defined by:

$\begin{eqnarray*}P_1 &=& 1\\P_2 &=& 1\\P_3 &=& 1\\P_n &=& P_{n-2} + P_{n-3}\end{eqnarray*}$

The difference is that the next term is the sum of the two terms before the previous term; the sum is "lagged" by an additional position in the sequence. Thus, its characteristic equation is:

$x^3-x-1 = 0$

To solve this, we must use Cardano's method. First, we make a substitution of the form

$x = u + \frac{a}u$

which we may do so long as $u \not = 0$ . This substitution gives us

Just testing

by Rosencrantz (Dummy text)
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