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

Richard Mathar mathar at strw.leidenuniv.nl
Mon Jun 22 13:15:05 CEST 2009

```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:

```