A002968 Number of pairings {(b(1), c(1)), (b(2), c(2)), ..., (b(n), c(n))} of the first 2n positive integers satisfying b(i) < c(i) and such that the 2n numbers c(i)+b(i) and c(i)-b(i) are all distinct.

1, 1, 0, 1, 8, 22, 51, 342, 2609, 16896, 99114, 876579, 8551800, 79595269, 764804085, 8905825760

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

Huff paper has a typographical error, a(8)=2669. - Sean A. Irvine, Dec 14 2014

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• R. Spira, Noncomplete residue systems, Problem 71-4, SIAM Rev., 14 (1972), 173ff.

Links

• R. K. Guy, Letter to G. B. Huff & N. J. A. Sloane, Aug 1974.
• G. B. Huff, On pairings of the first 2n natural numbers, Acta Arithmetica, 23 (1973), 117-126.
• D. A. Klarner, Letter to N. J. A. Sloane, Mar 1974.
• R. Spira, Noncomplete residue system Problem 71-4, SIAM Rev., 14 (1972), 173-174. (Annotated scanned copy)

Crossrefs

Cf. A007631.

Extensions

Better definition and values of a(11)-a(15) from Sean A. Irvine, Dec 14 2014

a(0)=1 prepended by Alois P. Heinz, Oct 05 2018