A collection of Fortran routines to calculate Wigner (Edmonds 1957)
or YLV62 (Yutsis et al 1962) 3n-j coefficients for any integer n.ge.1.


They are based-on recursion, combining algorithms (but not coding) of
Schulten & Gordon (1976) and Luscombe & Luban (1998), as detailed in
Badnell et al (2021).

Each file is self-contained, just compile and execute.
The interactive driver should be self-explanatory.

twig3jrm.f calculates the Wigner  3-j coefficients (a b c // d e f) by recursion on e.

twig3jrj.f calculates the Wigner  3-j coefficients (a b c // d e f) by recursion on a.

twig6jr.f  calculates the Wigner  6-j coefficients {a b c // d e f} by recursion on a.

twig9j.f   calculates the Wigner  9-j coefficient  {a b c // d e f // g h i} 
                                                                    using 6-j x3 summation.

twig3nj.f  calculates the Wigner 3n-j coefficient  {a_1...a_n // b_1...b_n // c_1...c_n}
                                                                    using 6-j xn sum.

tc3nj.f    calculates the YLV62  3n-j coefficients of the 1st & 2nd kind 
                                                   {a_1...a_n   //   b_1...b_n // c_1...c_n   }
                                                                    using 6-j xn sum.

N.B. twig3nj.f contains a subroutine (ylv2wig) which maps between YLV62-ordered 3n-j arguments
     and Wigner order, which might be of use.
N.B. tc3nj.f contains a subroutine (wig2ylv) which maps between Wigner-ordered 3n-j arguments
     and YLV62 order, which might be of use.


REFERENCES:
Badnell N. R., Guzman F., Brodie S., Williams R. J. R., van Hoof P. A. M., Chatzikos M., 
               Ferland G. J., 2021 MNRAS, 507, 2922
Edmonds A. R., 1957 Angular Momentum in Quantum Mechanics, Princeton, NJ
Luscombe J. H., Luban M., 1998, Phys.Rev.E, 57, 7274
Schulten K., Gordon R. G., 1976, Comput.Phys.Commun., 11, 269
Yutsis A. P., Levinson I. B., Vanagas V. V., 1962 "Mathematical Apparatus of the Theory
            of Angular Momentum" Israel Program for Scientific Translations: Jerusalem