[QUOTE=mart_r;248780]So, the exact number is
[SPOILER]267434832997843047170816167609147911673149856178056366366182308284997409845376
out of
653318623500070906096690267158057820537143710472954871543071966369497141477376
[/SPOILER][/QUOTE]

Confirmed. Here it is my much faster version for your problem:

[code]
dice2(w)=ct=6^w;P=vector(w+1,i,(i-1)!);\
for(a=0,w,for(f=a,2*a-1,\
for(b=max(a,w-a-4*f),min(f,(w-a-f)\4),\
for(c=max(b,w-a-b-3*f),min(f,(w-a-b-f)\3),\
for(d=max(c,w-a-b-c-2*f),min(f,(w-a-b-c-f)\2),\
e=w-a-b-c-d-f;\
if(e>=d&&e<=f,sub=720*P[w+1]/(P[a+1]*P[b+1]*P[c+1]*P[d+1]*P[e+1]*P[f+1]);\
v=[a,b,c,d,e,f];s=1;for(i=2,6,if(v[i]==v[i-1],s++,sub\=P[s+1];s=1));\
ct-=sub\P[s+1]))))));return(ct)
[/code]