A339288 Number of essentially series oriented series-parallel networks with n elements and without multiple unit elements in parallel.

0, 1, 1, 3, 8, 22, 64, 189, 577, 1788, 5642, 18016, 58213, 189792, 623913, 2065219, 6878429, 23032917, 77500237, 261892491, 888439320, 3024510467, 10329241959, 35379140285, 121502993735, 418306868672, 1443409882944, 4991122973019, 17292424070839, 60021140494647, 208684858267921

Offset

1,4

Comments

See A339290 for additional details.

Links

Table of n, a(n) for n=1..31.

Formula

G.f.: P(x)^2/(1 - P(x)) where P(x) is the g.f. of A339289.

G.f.: B(x)^2/(1 + B(x)) where B(x) is the g.f. of A339290.

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(2) = 1: (oo).
a(3) = 1: (ooo).
a(4) = 3: (oooo), (o(o|oo)), ((o|oo)o).
a(5) = 8: (ooooo), (oo(o|oo)), (o(o|oo)o), ((o|oo)oo), (o(o|ooo)), (o(oo|oo)), ((o|ooo)o), ((oo|oo)o).

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = Z + (1 + Z)*x*Ser(EulerT( Vec(p^2/(1+p), -n) ))); Vec(p - p/(1+p), -n)}

Crossrefs

Cf. A339154, A339289, A339290, A339291 (achiral), A339294 (unoriented).

Sequence in context: A164934 A047926 A192681 * A014138 A099324 A372528

Adjacent sequences: A339285 A339286 A339287 * A339289 A339290 A339291

Keyword

nonn

Author

Andrew Howroyd, Dec 07 2020

Status

approved