A002638 a(n) = (number of nonisomorphic nontransitive prime tournaments on n nodes) - Moebius(n).

-1, 1, 2, 3, 12, 52, 456, 6873, 191532, 9733032, 903753248, 154108311046, 48542114686912, 28401423719121392, 31021002160355166800, 63530415842308265086523, 244912778438520759443245824, 1783398846284777975419599903948, 24605641171260376770598003978281472

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..76
• J. W. Moon and M. Goldberg, On the composition of two tournaments, Duke Mathematical Journal, vol.37, no.2 (1970), pp.323-332. (subscription required)
• J. W. Moon and M. Goldberg, On the composition of two tournaments, Duke Mathematical Journal 37.2 (1970): 323-332. [Annotated scans of pages 331 and 332 only]
• Index entries for sequences related to tournaments

Crossrefs

Cf. A000568, A008683, A259106.

Formula

a(1) = -1, a(n) = A000568(n) - Sum_{d|n, d!=1, d!=n} a(d) * A000568(n / d). - Sean A. Irvine, Oct 19 2015

a(n) = A259106(n) - A008683(n). - Pontus von Brömssen, Oct 03 2020

Extensions

Definition clarified by N. J. A. Sloane, Jun 23 2015

More terms from Sean A. Irvine, Oct 19 2015

a(19) from Pontus von Brömssen, Oct 03 2020