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
langford_bp.pl B-Prolog
langford.co Comet
langford.ecl ECLiPSe
Langford-direct.essence Essence
Langford-positional.essence Essence
Langford_jacop.scala JaCoP/Scala
langford2.mzn MiniZinc
Langford.py Numberjack
langford.cs or-tools/C#
langford_ortools.py or-tools/Python
Langford_oscar.scala OscaR
langford.pi Picat
ROD.pl 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.

langford_sicstus.pl SICStus Prolog
sicstus_csplib024.pl SICStus Prolog