Langford strings

Question

Challenge description

A Langford string of order N is defined as follows:

• The length of the string is equal to 2*N,
• The string contains first N letters of the English alphabet, each letter appearing twice,
• For each pair of the same letters, there are M letters between them, where M is that letter's position in the alphabet (A = 1, B = 2, ..., Z = 26).

For instance, the only two possible Langford strings of order 3 are BCABAC and CABACB. As you can see, in both of these strings there is one letter between two A's, two letters between B's and three letters between C's. Given a positive integer N, output all Langford strings of order N (in any reasonable format: print them one by one separated by a newline, return a list/array...).

Sample inputs / outputs

3: [CABACB, BCABAC]
4: [DACABDCB, BCDBACAD]
5: # no output #
7: [GCFBECBDGFEADA, GBFCBDECGFDAEA, GBDFBCEDGCFAEA, GCAFACDEGBFDBE, GADAFCEDGCBFEB, GACAFDCEGBDFBE, GDAEAFDCGEBCFB, GBDEBFCDGECAFA, EGBFCBEDCGFADA, CGDFCBEDBGFAEA, EGDAFAEDCGBFCB, EGBCFBECDGAFAD, AGABFDBECGDFCE, EGADAFECDGBCFB, AGABEFBCDGECFD, BGDBCEFDCGAEAF, FBGDBCEFDCGAEA, BFGBAEADFCGEDC, CFGACADEFBGDBE, EAGAFBEDBCGFDC, BCGBFCEADAGFED, DAGAFDBECBGFCE, EBGCBFECDAGAFD, CEGDCFBEDBGAFA, CEGBCFBEDAGAFD, BDGBCFDECAGAFE, EFAGACEDFCBGDB, DFAGADEBFCBGEC, AFAGBDEBFCDGEC, DFAGADCEFBCGBE, ECFGBCEBDFAGAD, DEFGADAECFBGCB, CDFGCBDEBFAGAE, EBDGBFEDACAGFC, CDEGCFDAEABGFB, AEAGCDFECBDGBF, FAEAGCDFECBDGB, DFCEGDCBFEBAGA, BFCBGDCEFADAGE, ECFDGCEBDFBAGA, DAFAGDCEBFCBGE, BCFBGCDEAFADGE, AEAFGBDEBCFDGC, ADAFGCDEBCFBGE, AFACEGDCFBEDBG, BFCBEGCDFAEADG, EBFDBGECDFACAG, BEFBCGDECFADAG, EBDFBGEDCAFACG, AEAFCGDECBFDBG, AEADFGCEDBCFBG, ADAEFGDBCEBFCG]
12: # <216288 strings> #

Notes

• Langford strings of order N can only be produced when N ≡ 0 (mod 4) or N ≡ 3 (mod 4),
• You can use both lower-case and upper-case letters,
• You may use subsequent numbers as well (012... or 123... instead of ABC...)
• Order of strings in which they should appear as output is unspecified,
• Output can be quite lengthy (for instance, there are over 5 trillion distinct Langford strings of order 20), so your program doesn't actually need to output them all, but it has to work in theory (given enough time and memory).
• This challenge has been taken from /r/dailyprogrammer, all credit goes to /u/XenophonOfAthens

Answer 1

CJam (23 bytes)

{,2*e!{__f{\a/1=,(}=},}

Online demo. This is an anonymous block (function) which takes input on the stack and leaves output on the stack in the form of an array of arrays of 0-based sequential integers.

Answer 2

Brachylog, 43 bytes

:1fd.
ybB:1jp.,B:[.]z:2a
:3f-+$_~h?
t:.m~h?

Try it online!