|
|
A339155
|
|
Number of essentially parallel oriented series-parallel networks with n elements and without unit elements in parallel.
|
|
3
|
|
|
1, 0, 0, 1, 1, 3, 5, 13, 29, 70, 165, 409, 1001, 2505, 6278, 15904, 40447, 103567, 266229, 687668, 1782573, 4637731, 12103112, 31679212, 83135973, 218713492, 576683119, 1523740365, 4033915677, 10698680606, 28422818782, 75629586540, 201539697208, 537818080714
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
A series configuration is an ordered concatenation of two or more parallel configurations and a parallel configuration is the unit element or a multiset of two or more series configurations. a(n) is the number of parallel configurations with n unit elements.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: B(x)/(1 + B(x)) where B(x) is the g.f. of A339156.
|
|
EXAMPLE
|
In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
a(1) = 1: (o).
a(4) = 1: (oo|oo).
a(5) = 1: (oo|ooo).
a(6) = 3: (oo|oooo), (ooo|ooo), (oo|oo|oo).
a(7) = 4: (oo|ooooo), (oo|o(oo|oo)), (oo|(oo|oo)o), (ooo|oooo), (oo|oo|ooo).
|
|
PROG
|
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(p=x+O(x^2)); for(n=2, n, p=x+x*Ser(EulerT(Vec(p^2/(1+p), -n)))); Vec(1 - 1/(1+p))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|