A000083 Number of mixed Husimi trees with n nodes; or polygonal cacti with bridges. (Formerly M1191 N0461)

1, 1, 1, 2, 4, 9, 23, 63, 188, 596, 1979, 6804, 24118, 87379, 322652, 1209808, 4596158, 17657037, 68497898, 268006183, 1056597059, 4193905901, 16748682185, 67258011248, 271452424286, 1100632738565, 4481533246014

Offset

0,4

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

Christian G. Bower, Table of n, a(n) for n = 0..500

G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory of graphs III, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.

Eric Weisstein's World of Mathematics, Cactus Graph

Index entries for sequences related to cacti

Index entries for sequences related to trees

Formula

G.f.: A(x) = B(x) + C(x) - B(x)*D(x), where B, C, D respectively are g.f.s of A000237, A035349, A035350. - Christian G. Bower, Nov 15 1998

Crossrefs

Cf. A000237, A000314, A035082, A035349-A035357.

Sequence in context: A058585 A001573 A135307 * A092668 A164039 A362549

Adjacent sequences: A000080 A000081 A000082 * A000084 A000085 A000086

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Nov 15 1998

Status

approved