A339289 Number of essentially parallel oriented series-parallel networks with n elements and without multiple unit elements in parallel.

1, 0, 1, 2, 5, 14, 39, 117, 353, 1099, 3458, 11066, 35738, 116622, 383448, 1269869, 4230557, 14170956, 47693457, 161207066, 546987882, 1862464911, 6361729689, 21793247587, 74855427331, 257743707769, 889477338903, 3076038022778, 10658447368514, 36998473045302

Offset

1,4

Comments

See A339290 for additional details.

Links

Table of n, a(n) for n=1..30.

Formula

G.f.: B(x)/(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(1) = 1: (o).
a(3) = 1: (o|oo).
a(4) = 2: (o|ooo), (oo|oo).
a(5) = 5: (o|oooo), (o|o(o|oo)), (o|(o|oo)o), (oo|ooo), (o|oo|oo).

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(1-1/(1+p))}

Crossrefs

Cf. A339155, A339288, A339290, A339292 (achiral), A339295 (unoriented).

Sequence in context: A102406 A307754 A151409 * A003054 A317553 A370723

Adjacent sequences: A339286 A339287 A339288 * A339290 A339291 A339292

Keyword

nonn

Author

Andrew Howroyd, Dec 07 2020

Status

approved