sqlite update a column with itself

I got a table like this

a  b  c
-- -- -- 
1  1  10
2  1  0
3  1  0
4  4  20
5  4  0
6  4  0

The b column 'points' to 'a', a bit like if a is the parent. c was computed. Now I need to propagate the parent c value to their children.

The result would be

a  b  c
-- -- -- 
1  1  10
2  1  10
3  1  10
4  4  20
5  4  20
6  4  20

I can't make an UPDATE/SELECT combo that works

So far I got a SELECT that procuce the c column I'd like to get

select t1.c  from t t1 join t t2 on t1.a=t2.b;
c
----------
10
10
10
20
20
20

But I dunno how to stuff that into c

Thanx in advance Cheers, phi