The first part of this coursework will allow us to use Python to explore difference equations. We'll model a homogeneous difference equation using its list of negated non$-$leading coefficients, so $2,4$ represents the equation: $x_{n+2}=2x_n+4x_{n+1}.$ We'll also model the initial conditions as a list, so $1,2$ represents the initial conditions $x_0=1,x_1=2.($Notice that the two lists need to have the same length.$)$

A$1$ Write a function DifferenceSequence$($Equation$,$ InitialConditions, NumberOfTerms$)$ which takes as inputs lists representing a homogeneous linear difference equation, and some corresponding initial conditions, and an integer $n$ representing a $($large$)$ number of terms, and outputs a list of the first $n$ terms of the solution: $x_0,x_1,$dots,$x_{n-1}.$

Hint: create a solution list which consists of the initial conditions. Set up a loop whose length is the number of terms you need to calculate. At each stage compute the new term by taking the dot product of the coefficients and last few terms in the solution list, and then append it to the end of the solution list.