bartc <b...@freeuk.com> writes: > On 10/03/2018 20:06, Ben Bacarisse wrote: >>> On 10/03/2018 14:23, Ben Bacarisse wrote: <snip> >>>> Off topic: I knocked up this Haskell version as a proof-of-concept: >>>> >>>> import Data.List >>>> >>>> pn n l = pn' n (map (:[]) l) >>>> where pn' n lists | n == 1 = lists >>>> | otherwise = diag (pn' (n-1) lists) lists >>>> diag l1 l2 = zipWith (++) (concat (inits l1)) >>>> (concat (map reverse (inits >>>> l2))) >>>> <snip> >> but, as I've said, the order of the results is not the usual one (except >> for pairs).
> OK. I ran it like this: > > main = print (take 20 (pn 3 [1..])) > > But I'm trying to understand the patterns in the sequence. If I use: > > main = print (take 50 (pn 2 [1..])) > > then group the results into sets of 1, 2, 3, etc pairs, showing each > group on a new line, then this gives sequences which are equivalent to > the diagonals of the OP's 2D grid. (Except they don't alternate in > direction; is that what you mean?) Yes, the pattern for pairs (pn 2 [1..]) is the normal one (one of them anyway). In the 2D grid the diagonals are lines of equal sum (for a numeric grid, of course) and all the pairs that sum to x appear before those that sum to x+1: *Main> take 28 $ map sum $ pn 2 [1..] [2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8] The recursive step breaks this rule. I'm sure there's a better rule, but it's getting more and more off-topic... -- Ben. -- https://mail.python.org/mailman/listinfo/python-list
