Questions on sums of squares/PARI

[franktaw at netscape.net]

It appears that the corresponding sequence for sums of triangular 
numbers n(n+1)/2 is

20, 119, 461, 594, 1172

Franklin T. Adams-Watters

-----Original Message-----
From: franktaw at netscape.net

I have just submitted the following two sequences:

%I A138554
%S A138554 
0,1,2,3,2,3,4,5,4,3,4,5,6,5,6,7,4,5,6,7,6,7,8,9,8,5,6,7,8,7,8,9,8,9,8,9,6
 ,7,8,9,8,
9,10,11,10,9,10,11,12,7,8,9,10,9,10,11,12,11,10,11,12,11,12,13,8,9,10,11,
 10,11,12,
13,12,11,12,13,14,13,14,15,12,9,10,11,12,11,12,13,14,13,12,13,14,15,14,15
 ,16,13,
14,15,10,11,12,13,12,13,14,15,14,13,14,15,16,15,16,17,14,15,16,17,16
%N A138554 Minimum value of sum k_i when sum k_i^2 = n.
%e A138554 32 = 4^2 + 4^2, and 4+4 = 8.  Using 5, the best we can do is 
32 = 5^2
+ 2^2 + 1^2 + 1^2 + 1^2, and 5+2+1+1+1 = 10, so a(32) = 8.
%o A138554 (PARI) sslist(n) = {local(r,i,v,t);
r=vector(n+1,k,0);
for(k=1,n,v=k;i=1;while(i^2<=k,t=r[k-i^2+1]+i;if(t<v,v=t);i++);r[k+1]=v);

r}
%Y A138554 Cf A063772, A138555, A001156.
%O A138554 0
%K A138554 ,nonn,

%I A138555
%S A138555
32,61,136,193,218,219,320,464,673,776,777,884,1021,1145,1417,1440,1744,21
 94,2195,
2285,2696,2697,2797,3361,3560,4321,4880,5156,5618,5619,5765,7048,8424,957
7,9770,
9771,11216,11217,12541,13856,15817,20129,21312,22480,24961
%N A138555 Indices where A138554 requires only squares < 
floor(sqrt(n))^2.
%C A138555 Express n = sum k_i^2 so as to minimize sum k_i.  There may 
be more
than one such sum; for example 12 = 3^2 + 1^2 + 1^2 + 1^2 = 2^2 + 2^2 + 
2^2.  If
every such minimal sum uses squares only of numbers < floor(sqrt(n)), n 
is included in this
sequence.
%o A138555 (PARI) dsslist(n) = {local(r, i, j, v, t, d);
r=vector(n+1,k,0);
d=[];
for(k=1,n,v=k;i=1;j=0;
 while(i^2<=k,t=r[k-i^2+1]+i;if(t<=v,v=t;j=i);i++);
 r[k+1]=v;if(j<i-1,d=concat(d,[k])));
d}
%O A138555 1
%K A138555 ,nonn,

Based on the PARI program shown, these are the only values of A138555
up to 200000.
I'm wondering if this is correct, or some kind of bug in PARI.  Could 
someone program it
with some other tool to verify (and perhaps extend) these results?

If this is correct, could it be that the sequence is finite?