Understanding `NestList` with multiple functions

Question

General question

For a function f[n, a], where a is a list and n is a whole number, what is the correct syntax for

f[n - 5, f[n - 4, f[n - 3, f[n - 2, f[n - 1, f[n, a]]]]]]

?

All I want to do is

fg[n_, w_] := f1@ff[n, w]
fg[n - 2, fg[n - 1, fg[n, list]]]

as shown above, which works, but I am having to manually write out n-3,n-2,n-1,...

Have tried

fg[n_][w_] := f1@ff[n, w]
NestList[fg[n], list, 3]

but doesn't quite work. I think it needs a #-1 in there somewhere, that is applied to the n, but not sure on syntax.

Wait ... do you need help with NestList[] or with that code? — Dr. belisarius, Nov 18 '14 at 20:57
@martin I'm also having trouble understanding what you're trying to do here.. — Kris, Nov 18 '14 at 21:00
@belisarius It is just the last line I need help with - the fg[n - 2, fg[n - 1, fg[n, list]]] bit — martin, Nov 18 '14 at 21:05
Just need another way of writing fg[n - 2, fg[n - 1, fg[n, list]]] — martin, Nov 18 '14 at 21:08
@belisarius can't get that to work - not sure what I am doing wrong... — martin, Nov 18 '14 at 21:18
@belisarius have tried that - is that for fg[n_][w_] := f1@ff[n, w] or fg[n_, w_] := f1@ff[n, w]? — martin, Nov 18 '14 at 21:26
@belisarius there might have been a problem with the example code - up[dated so should work now. — martin, Nov 18 '14 at 21:31
@Kris there might have been a problem with the example code - up[dated so should work now. — martin, Nov 18 '14 at 21:32

Kris · Answer 1 · 2014-11-19T13:51:30.237

4

Could it be that you're looking for the function Fold rather than Nest?

Fold[f[n - #2, #1] &, a, Range[5]]

f[-5 + n, f[-4 + n, f[-3 + n, f[-2 + n, f[-1 + n, a]]]]]

edited Nov 19 '14 at 13:51

answered Nov 19 '14 at 12:00

Kris

1

+1, maybe better Fold[g[#2, #] &, a, Range[n, n - 2, -1]]. – Kuba Nov 19 '14 at 12:09
@Kuma Thanks, I agree that a one-liner is nicer. I updated the answer – Kris Nov 19 '14 at 13:52

score 1 · Accepted Answer · answered Nov 18 '14 at 21:59

1

Last @ Nest[{ #[[1]] - 1,  f1[ ff[ #[[1]], #[[2]] ] ] } &,
            {n, list}, 
            3]

f1[ff[-2 + n, f1[ff[-1 + n, f1[ff[n, list]]]]]]

answered Nov 18 '14 at 21:59

Kuba