

A058387


Number of seriesparallel networks with n unlabeled edges, multiple edges not allowed.


4



0, 1, 1, 2, 4, 8, 18, 40, 94, 224, 548, 1356, 3418, 8692, 22352, 57932, 151312, 397628, 1050992, 2791516, 7447972, 19950628, 53635310, 144664640, 391358274, 1061628772, 2887113478, 7869761108, 21497678430, 58841838912, 161356288874
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OFFSET

0,4


COMMENTS

This is a seriesparallel network: oo; all other seriesparallel networks are obtained by connecting two seriesparallel networks in series or in parallel. See A000084 for examples.
Order is not considered significant in series configurations.  Andrew Howroyd, Dec 22 2020


REFERENCES

J. W. Moon, Some enumerative results on seriesparallel networks, Annals Discrete Math., 33 (1987), 199226 (the sequence v_n).


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500
Index entries for sequences mentioned in Moon (1987)
S. R. Finch, Seriesparallel networks
S. R. Finch, Seriesparallel networks, July 7, 2003. [Cached copy, with permission of the author]


FORMULA

a(n) = A058385(n) + A058386(n).


EXAMPLE

From Andrew Howroyd, Dec 22 2020: (Start)
In the following examples, elements in series are juxtaposed and elements in parallel are separated by ''. The unit element (an edge) is denoted by 'o'.
a(1) = 1: (o).
a(2) = 1: (oo).
a(3) = 2: (ooo), (ooo).
a(4) = 4: (oooo), (o(ooo)), (oooo), (oooo).
a(5) = 8: (ooooo), (oo(ooo)), (o(oooo)), (o(oooo)), (ooooo), (oo(ooo)), (ooooo), (ooooo).
(End)


PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))1, #v)}
seq(n)={my(s=p=vector(n)); p[1]=1; for(n=2, n, s[n]=EulerT(p[1..n])[n]; p[n]=vecsum(EulerT(s[1..n])[n1..n])s[n]); concat([0], p+s)} \\ Andrew Howroyd, Dec 22 2020


CROSSREFS

A000084 is the case that multiple edges are allowed.
A058381 is the case that edges are labeled.
A339290 is the case that order is significant in series configurations.
Cf. A058385, A058386, A000311, A000669, A006351.
Sequence in context: A000967 A288309 A096813 * A330052 A317787 A019231
Adjacent sequences: A058384 A058385 A058386 * A058388 A058389 A058390


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane, Dec 20 2000


STATUS

approved



