A339153 Number of nonequivalent series-parallel networks with n elements and without unit elements in parallel.

1, 1, 1, 2, 3, 6, 10, 20, 37, 74, 144, 295, 594, 1229, 2540, 5324, 11177, 23684, 50326, 107593, 230743, 497008, 1073667, 2327213, 5057433, 11020414, 24068945, 52685541, 115555511, 253933732, 558993308, 1232569467, 2721958234, 6019784562, 13331192017, 29560633824

Offset

1,4

Comments

Equivalence is up to rearrangement of the order of elements in both series and parallel configurations.

A series configuration is a multiset of two or more parallel configurations and a parallel configuration is a multiset of two or more series configurations. The unit element is considered to be a parallel configuration.

Links

Table of n, a(n) for n=1..36.

Formula

a(n) = A339151(n) + A339152(n).

Euler transform of A339152.

Euler transform of A339151 gives this sequence with a(1) = 0.

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(2) = 1: (oo).
a(3) = 1: (ooo).
a(4) = 2: (oooo), (oo|oo).
a(5) = 3: (ooooo), (o(oo|oo)), (oo|ooo).
a(6) = 6: (oooooo), (oo(oo|oo)), (o(oo|ooo)), (oo|oooo), (ooo|ooo), (oo|oo|oo).

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(S=vector(n), P=vector(n)); P[1]=1; for(n=2, #S, my(t=EulerT(S[1..n])[n]); S[n]=EulerT(P[1..n])[n]; P[n]=t); S+P}

Crossrefs

Cf. A000669, A339151, A339152.

Sequence in context: A045690 A007148 A093371 * A003214 A331693 A123423

Adjacent sequences: A339150 A339151 A339152 * A339154 A339155 A339156

Keyword

nonn

Author

Andrew Howroyd, Nov 26 2020

Status

approved