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Number of pairings of the first 2n positive integers so that the absolute differences of each pair are different.
9

%I #33 Feb 19 2020 01:15:18

%S 1,1,1,5,29,145,957,8397,85169,944221,11639417,160699437,2430145085,

%T 39776366397,703161838717,13369111112753,271734091323897

%N Number of pairings of the first 2n positive integers so that the absolute differences of each pair are different.

%C Number of perfect Skolem-type sequences.

%H Edward Moody, <a href="https://github.com/EdwardMGraphite/generalised-langford">Java program for calculating entries in this sequence and A322178</a>

%H G. Nordh, <a href="https://arxiv.org/abs/math/0506155">Perfect Skolem sequences</a>, arXiv:math/0506155 [math.CO], 2005.

%e a(3)=5 since the 5 pairings of {1, 2, 3, 4, 5, 6} are {1, 3} {2, 6} {4, 5}, {1, 5} {2, 3} {4, 6}, {1, 5} {2, 4} {3, 6}, {1, 4} {2, 6} {3, 5}, {1, 6} {2, 5} {3, 4}.

%Y Cf. A261516, A261517, A322178.

%K nonn,more

%O 0,4

%A _Erich Friedman_, May 08 2001

%E Offset corrected by _Alois P. Heinz_, Sep 14 2015

%E a(14) from _Fausto A. C. Cariboni_, Mar 03 2017

%E a(15) from _Fausto A. C. Cariboni_, Apr 10 2017

%E a(16) from _Edward Moody_, Feb 17 2020