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A339151
Number of essentially series nonequivalent series-parallel networks with n elements and without unit elements in parallel.
3
0, 1, 1, 1, 2, 3, 6, 11, 21, 41, 81, 164, 333, 684, 1417, 2965, 6229, 13182, 28019, 59862, 128376, 276408, 597041, 1293763, 2811181, 6124479, 13374201, 29270703, 64191331, 141041901, 310444472, 684445543, 1511345542, 3342101662, 7400605768, 16408670095
OFFSET
1,5
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.
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) = 1: (oooo).
a(5) = 2: (ooooo), (o(oo|oo)).
a(6) = 3: (oooooo), (oo(oo|oo)), (o(oo|ooo)).
a(7) = 6: (ooooooo), (ooo(oo|oo)), (oo(oo|ooo)), (o(oo|oooo)), (o(ooo|ooo)), (o(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}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 26 2020
STATUS
approved