Some Mathematica code for counting number of solutions by brute force (and links to some previous solutions).

File Type Notes
Langford.aim AIMMS+CP
langford.lp4 ASP Gringo 4 B-Prolog Comet
langford.ecl ECLiPSe
Langford-direct.essence Essence
Langford-positional.essence Essence
Langford_jacop.scala JaCoP/Scala
langford2.mzn MiniZinc Numberjack
langford.cs or-tools/C# or-tools/Python
Langford_oscar.scala OscaR
langford.pi Picat pl

A Perl program written by John Miller based on a pattern found by Roy O. Davies that generates a single Langford sequence (for large n). Counting the number of sequences is likely to be intractable. SICStus Prolog SICStus Prolog