[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]

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: