[seqfan] Re: The weight puzzle sequence

W. Edwin Clark wclark at mail.usf.edu
Tue Aug 24 22:38:28 CEST 2010


On Tue, Aug 24, 2010 at 3:14 PM, Richard Mathar
<mathar at strw.leidenuniv.nl>wrote:

>
>
>
> So the size-sequence starts 1,2,2,3,3,3,4,4,4,4,4,4,5,5,5,5


> Independent confirmations certainly desired!
>

A truly brute force Maple program (see below) agrees with you:

 > with(combinat):

> isGood:=proc(T)
> local ps,x,S;
> S:={}:
> ps:=powerset(T):
> for x in ps do
>  S:=S union {add(j,j=x)}:
> od:
> if nops(S) = nops(ps) then return true; else return false; fi;
> end proc:

> for n from 1 to 20 do
>   a(n):=0;
>   for T in powerset(n) do
>     if isGood(T) = true and nops(T) > a(n) then a(n):=nops(T); fi;
>   od;
> od:
> seq(a(n),n=1..16);

            1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5



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