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A003081 Number of triangular cacti with 2n+1 nodes (n triangles).
(Formerly M1152)
3
1, 1, 1, 2, 4, 8, 19, 48, 126, 355, 1037, 3124, 9676, 30604, 98473, 321572, 1063146, 3552563, 11982142, 40746208, 139573646, 481232759, 1669024720, 5819537836, 20390462732, 71762924354, 253601229046, 899586777908, 3202234779826, 11435967528286, 40964243249727 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 306, (4.2.35).

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 73, (3.4.21).

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1 (1992) pp. 53-80.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)

Index entries for sequences related to cacti

FORMULA

a(n)=b(2n+1). A003080(n)=c(2n+1).

G.f.: B(x)=C(x)+(C(x^3)-C(x)^3)/3.

CROSSREFS

Cf. A003080, A034940, A034941.

Sequence in context: A099526 A005703 A172383 * A100133 A099598 A269023

Adjacent sequences:  A003078 A003079 A003080 * A003082 A003083 A003084

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended with formula by Christian G. Bower, 10/98

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)