00:01
So we need to find the, so we need to find a of 3 and a of 4, or a of n is just the number of subsets in a given set s.
00:23
Okay, the number of subsets that are, that do not have consecutive contributors.
00:29
Okay, so first, s of 3 is just 1, 2, it has these 3 elements, and i need its subsets, so we'll have the empty set.
00:52
You'll have 1, 2, 3, 1 2, 1 3, 1 3, 3, 1 3, 3, 2, 3, 1 3, 3, 2, 3, 1 3, 3, 2, 3, 1, 3, 3.
01:13
So these are all of the sets for all of these subsets for sf3 and so a f3 which is the subsets that do not have consecutive numbers so this has consecutive this has consecutive this has the empty set the set containing 1, set containing 2, set containing 3, second 103, so this is the first one and now we're going to consider when n is 4 so a 4 is the same thing as the set with one two three four elements and so this is going to be a lot because we have so two to the fourth we have four elements is going to be 16 so we're expecting 16 subsets okay so we're going to compute this let's see so we need the empty set we need one two two, three.
03:01
I'm going to write out all of the, i'm going to pass, write out all of the subsets, and then we'll continue...