[seqfan] Re: Sums of values of A113907. Sums of dimensions of the five sporadic Lie groups. Dimensions of direct products of sporadic Lie groups.

[Jonathan Post]

Thank you, Richard Mathar.  Looking at my handwritten text, I had
indeed found a(30) = 147 and failed to type it in the email.

I'm close to submitting the sequence, or asking you if you should like
to, with the comment by Robert Gerbicz (i.e. giving 327 as the last
value shown and commenting that all greater integers are also in the
sequence) and your code.

I take it that this would be preferable to giving the complement of
the sequence?

How many values are there from 14 through 327 inclusive?

Best,

Jonathan Vos Post

On Mon, Jun 22, 2009 at 4:15 AM, Richard
Mathar<mathar at strw.leidenuniv.nl> wrote:
>
> In http://list.seqfan.eu/pipermail/seqfan/2009-June/001734.html we read
>
> jvp> 14, 28, 42, 52, 56, 66, 70, 78, 80, 84, 92, 94, 98, 104, 106, 108,
> jvp> 112, 118, 120, 122, 126, 130, 132, 133, 134, 136, 140, 144, 146, 148,
> jvp> 150, 154, 156, 158, 160, 161, 162, 164
> jvp>
> jvp> Sorry if I've made some errors doing this by hand. Am I getting
> jvp> anything right here, in arithmetic and interpretation?
> jvp>
> jvp> Sums of values of A113907.  Sums of dimensions of the five sporadic
> jvp> Lie groups. Dimensions of direct products of sporadic Lie groups.
> jvp> Integers of the form 14a + 52b + 78c + 133d + 248e for nonnegative
> jvp> integers a, b, c, d.
>
> 147 is missing in the list, returned by a=1, b=c=0, d=1, e=0.
>
> The Maple coding is:
>
> L := [14,52,78,133,248] ;
>
> # check whether n is a linear combination of op(..,L) with
> # some non-negative a,b,c,d,e
> frob := proc(n,L)
>        local a,b,c,d,e,nres ;
>        for a from 0 do
>                if a*op(1,L) > n then
>                        break;
>                fi;
>                for b from 0 do
>                        if a*op(1,L)+b*op(2,L) > n then
>                                break;
>                        fi;
>                        for c from 0 do
>                                if a*op(1,L)+b*op(2,L)+c*op(3,L) > n then
>                                        break;
>                                fi;
>                                for d from 0 do
>                                        if a*op(1,L)+b*op(2,L)+c*op(3,L)+d*op(4,L) > n then
>                                                break;
>                                        fi;
>                                        nres := n-a*op(1,L)-b*op(2,L)-c*op(3,L)-d*op(4,L) ;
>                                        if nres < 0 then
>                                                break;
>                                        fi;
>                                        if nres = 0 then
>                                                RETURN([a,b,c,d,0]) ;
>                                        fi;
>                                        if ( nres mod op(5,L) ) = 0 then
>                                                RETURN([a,b,c,d,nres/op(5,L)]) ;
>                                        fi;
>                                od:
>                        od;
>                od:
>        od:
>        RETURN([]) ;
> end:
>
> for n from 14 to 200 do
>        f := frob(n,L) ;
>        if f <> [] then
>                print(n,f) ;
>        fi;
> od:
>
>
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