A002638 a(n) = (number of nonisomorphic nontransitive prime tournaments on n nodes) - Moebius(n). (Formerly M0913 N0345)

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

Offset

1,3

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

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

Crossrefs

Cf. A000568, A008683, A259106.

Sequence in context: A307957 A307956 A358716 * A027072 A083746 A025231

Adjacent sequences: A002635 A002636 A002637 * A002639 A002640 A002641

Keyword

sign

Author

N. J. A. Sloane

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

Status

approved