Good day,
I am finding out the recurrence relationship for a checkboard 2xn. I got 1-squares(1x1) and L shape, 3-squares to choose from to cover the table. n>=1
So a0= 1 since its just two 1-squares and a1= 5 (all 1-squares + 4 ways to rotate one L-square and fill the rest with 1-squares ).
Next, I take a2 and as always; one way to choose all 1-squares, eight ways to use one L-square and since this is just two versions of the previous checkboard (4 ways + 4 ways), two ways to use two L-squares a3 = 1 + 8 + 2 =11 ways.
From this a4 = 2*11+5 = 27 ways and the recurrance relationship is an=2a(n-1)+a(n-2)? I am on the right path here, right?
After I have found out the recurrence relationship I am supposed to use Rsolve to solve it and plot discrete plot.
iv1 = a[0]==1;
iv2 = a[1]=5;
rr= a[n] == 2a[n-1]+a[n-2];
sol = RSolve[{rr, iv1, iv2},a[n],n]
Here I am very lost. I read on Rsolve and I assume I can program it this way with rr as the recurrance relation(RR) and iv1 and iv2 as initial values. But, what does Rsolve do for me and how do I use the code for my discrete plot? I get the use of finding the RR, then I can find out the next element just by using the two former ones, but what about my RR am I trying to solve with Rsolve and what is it that my discrete plot will visualize about my RR?