Demo of ingredients

j1 = 3;

j2 = 2;

Tables

cgtable = Table[tmp[m1,m2],{m2,-j2-1,j2+1},{m1,-j1-1,j1+1}]

cgtable // TableForm

cgtable[[2,3]]

Arrays using functions

cg[-2,3] = 7;

cg[-2,3]

cg[-2,7]

Recursion relation I

Clear[v]

varray=Table[v[i],{i,-j1,j1}] // TableForm

For[i=-j1,i≤j1-1,i++, v[i]= v[i+1]+1]

varray=Table[v[i],{i,-j1,j1}] // TableForm

Recursion relation II

Clear[v]

varray=Table[v[i],{i,-j1,j1}] // TableForm

v[3] = 0;

For[i=-j1,i≤j1-1,i++, v[i]= v[i+1]+1]

varray=Table[v[i],{i,-j1,j1}] // TableForm

Recursion relation III

Clear[v]

For[i=-j1,i≤j1,i++, v[i]= x]

v[j1] = 0;

varray=Table[v[i],{i,-j1,j1}] // TableForm

For[i=-j1,i≤j1-1,i++, If[v[i]===x && v[i+1]=!=x,v[i]= v[i+1]+1]]

varray=Table[v[i],{i,-j1,j1}] // TableForm