OFFSET
0,4
COMMENTS
This is a series-parallel network: o-o; all other series-parallel networks are obtained by connecting two series-parallel 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 series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence v_n).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
S. R. Finch, Series-parallel networks
S. R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]
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), (o|oo).
a(4) = 4: (oooo), (o(o|oo)), (o|ooo), (oo|oo).
a(5) = 8: (ooooo), (oo(o|oo)), (o(o|ooo)), (o(oo|oo)), (o|oooo), (o|o(o|oo)), (oo|ooo), (o|oo|oo).
(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])[n-1..n])-s[n]); concat([0], p+s)} \\ Andrew Howroyd, Dec 22 2020
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
N. J. A. Sloane, Dec 20 2000
STATUS
approved