I have to set up a recursive formula for a sequence that gives the number of ways to take out and arrange lego bricks to a wall with the length of 2n knobs.
Some lego bricks have 6-knobs and some has 8-knobs.
I have calculated several values for n.
I have problems setting up a rule from a pattern. I cant even see the pattern from the integers I have.
I have the following values (starting from n = 6) :
1 - 2 - 1 - 1 - 3 - 3 - 2 - 4 - 6 - 5 - 6 - 10 - 11 - 11 - 16 - 21 - 22 - 27 - 37
Can you see any pattern or could it be that I have calculated wrong somehow? (pretty sure my calculation is correct thought).
How about this: a(n) = a(n-4) + a(n-3)