im trying to get the kth row in every list in the pascal list. For example pascal 4 would get the 4nd element in every row. So it would return 1,4,10,20... etc. I understand how to construct an infinite pascal list which is what outputs below, but im unsure of how to get a nth element in each nested list. any suggestions? i was thinking of using map, but im not necessarily mapping a function here which is throwing me off a bit. thank you.
// im trying to get pascal k to return the nth element of every row in the triangle
pascal n = map(\n -> ??) take n pascal
pascal_infite = [1] : map (\l -> zipWith (+) (l ++ [0]) (0:l)) pascal_infinite
To get the kth row:
>>> pascal_infinite !! 4
[1,4,6,4,1]
To get all rows from [0..k]:
>>> map (pascal_infinite !!) [0..4]
[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
To get all rows from [0..k] fast:
>>> take (4+1) pascal_infinite
[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]
Whoops, misread the question a bit. To get what you're asking for, you should probably construct just use the good old n choose k formula or something similar if you're concerned about speed.
If this is just an exercise, disregarding speed, here's one way:
pascal n = map (!! n) $ drop n pascal_infinite
Then simply sample a couple of the 4th elements:
>>> take 8 $ pascal (4-1)
[1,4,10,20,35,56,84,120]