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 A339152 Number of essentially parallel nonequivalent series-parallel networks with n elements and without unit elements in parallel. 3
 1, 0, 0, 1, 1, 3, 4, 9, 16, 33, 63, 131, 261, 545, 1123, 2359, 4948, 10502, 22307, 47731, 102367, 220600, 476626, 1033450, 2246252, 4895935, 10694744, 23414838, 51364180, 112891831, 248548836, 548123924, 1210612692, 2677682900, 5930586249, 13151963729, 29201456634 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 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..37. FORMULA Inverse Euler transform of A339153. 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)), (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(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); P} CROSSREFS Cf. A000669, A339151, A339153. Sequence in context: A093368 A278025 A095095 * A003611 A192115 A103295 Adjacent sequences: A339149 A339150 A339151 * A339153 A339154 A339155 KEYWORD nonn AUTHOR Andrew Howroyd, Nov 26 2020 STATUS approved

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Last modified August 13 02:28 EDT 2024. Contains 375113 sequences. (Running on oeis4.)