Counting the Number of Langford Skolem Pairings
Ali Assarpour, Amotz Bar-Noy, Ou Liu · arXiv (Cornell University) · 2015
We compute the exact number, L(n), of solutions to the Langford pairings problem for any positive integer n<29 and the exact number of solutions to the Nickerson variant of the problem, N(n), for any positive integer n<26. These numbers correspond to the sequences A014552, A059106 in Sloane's Online Encyclopedia of Integer Sequences. The exact value of these numbers were known for any positive integer n<27 for the A014552 sequence and for any positive integer n<24 for the A059106 sequence. First we report that the number of Langford pairings for n=27 is L(27)=111,683,611,098,764,903,232, and for n=28 it is L(28)=1,607,383,260,609,382,393,152. Next we report that the number of solutions for the Nickerson variant of Langford pairings for n=24 is N(24)=102,388,058,845,620,672 and for n=25 it is N(25)=1,317,281,759,888,482,688.