ab[n,m,q_]:=和[q[n-m-r,k],{r,1,m},{k,m+1-r,n-m-r}]
bb[n,m,q_]:=和[q[n-m-r,m-r],{r,1,m-1}]+和[q[n-m-r、k],{r,1,m-1},{k,m-r,n-m-r}]
cb[n,m,q_]:=和[q[n-m-r,m-1-r],{r,1,m-2}]
a[n,m]:=0/;n<=1 | | m<=0
a[n,m]:=a[n、m]=和[(k-m)p[n-m,k],{k,m+1,n-m}]+ab[n,m,b]+2ab[n、m,c]+和[(r-1)c[n-m-r,m+1-r],{r,2,m}]
b[1,1]=1;
b[n,m]:=0/;n<=1 | | m<=0
b[n,m]:=b[n、m]=2总和[p[n-m,k],{k,m,n-m}]+bb[n,m,b]+2bb[n、m、c]+2总和[(r-1)c[n-m-r,m-r],{r,2,m-1}]
c[n_,m_]:=0/;n<=1 | | m<=0
c[n,m]:=c[n、m]=p[n-m,m-1]+cb[n,m,b]+2cb[n、m,c]+和[(r-1)c[n-m-r,m-1-r],{r,2,m-2}]
p[n,m]:=a[n,m]+b[n,米]+c[n,姆]
表[Sum[p[n,m],{m,(n+1)/2}],{n,20}]