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. (Formerly M4494)

1, 1, 0, 1, 8, 22, 51, 342, 2609, 16896, 99114, 876579, 8551800, 79595269, 764804085, 8905825760, 112166089619, 1423772212734

Offset

0,5

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

Table of n, a(n) for n=0..17.

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.

Sequence in context: A048489 A124701 A369593 * A211530 A058404 A350123

Adjacent sequences: A002965 A002966 A002967 * A002969 A002970 A002971

Keyword

nonn,more

Author

N. J. A. Sloane

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

a(16)-a(17) from Martin Fuller, Dec 02 2025

Status

approved