In[]:=
k=8;​​Row[Table[{m[k-l],IntegerPart[(k-l)/k],(n-Sum[(s)m[s],{s,k-l+1,k}])/(k-l)},{l,0,k-3}],","]​​Clear[k]
Out[]=
m[8],1,
n
8
,m[7],0,
1
7
(n-8m[8]),m[6],0,
1
6
(n-7m[7]-8m[8]),m[5],0,
1
5
(n-6m[6]-7m[7]-8m[8]),m[4],0,
1
4
(n-5m[5]-6m[6]-7m[7]-8m[8]),m[3],0,
1
3
(n-4m[4]-5m[5]-6m[6]-7m[7]-8m[8])
In[]:=
k=5;​​p[n_,5]:=Sum[IntegerPart[(2+n-Sum[im[i],{i,3,k}])/2],{m[5],1,n/5},{m[4],0,(n-5m[5])/4},{m[3],0,(n-4m[4]-5m[5])/3}]​​p[7,5]​​Clear[k]
Out[]=
2
In[]:=
k=6;​​p[n_,6]:=SumIntegerPart[(2+n-Sum[im[i],{i,3,k}])/2],m[6],1,
n
6
,m[5],0,
1
5
(n-6m[6]),m[4],0,
1
4
(n-5m[5]-6m[6]),m[3],0,
1
3
(n-4m[4]-5m[5]-6m[6])​​p[9,6]​​Clear[k]
Out[]=
3
In[]:=
k=8;​​p[n_,8]:=SumIntegerPart[(2+n-Sum[im[i],{i,3,k}])/2],m[8],1,
n
8
,m[7],0,
1
7
(n-8m[8]),m[6],0,
1
6
(n-7m[7]-8m[8]),m[5],0,
1
5
(n-6m[6]-7m[7]-8m[8]),m[4],0,
1
4
(n-5m[5]-6m[6]-7m[7]-8m[8]),m[3],0,
1
3
(n-4m[4]-5m[5]-6m[6]-7m[7]-8m[8])​​p[11,8]​​Clear[k]
Out[]=
3