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 A339159 Number of achiral series-parallel networks with n elements. 5
 1, 2, 3, 7, 12, 29, 54, 130, 258, 616, 1274, 3030, 6458, 15287, 33335, 78694, 174587, 411469, 925246, 2179010, 4952389, 11662221, 26733827, 62980863, 145385388, 342766624, 795810810, 1878109984, 4381423357, 10352044123, 24247955489, 57362089607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A series configuration is the unit element or an ordered concatenation of two or more parallel configurations and a parallel configuration is the unit element or a multiset of two or more series configurations. a(n) is the number of series or parallel configurations with n unit elements that are invariant under the reversal of all contained series configurations. LINKS FORMULA a(n) = A339157(n) + A339158(n) for n > 1. EXAMPLE In the following examples of series-parallel networks, 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) = 2: (oo), (o|o). a(3) = 3: (ooo), (o|oo), (o|o|o), (o|ooo), (oo|oo), (o|o|oo), (o|o|o|o). a(4) = 7: (oooo), ((o|o)(o|o)), (o(o|o)o). PROG (PARI) \\ here B(n) gives A003430 as a power series. EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} B(n)={my(p=x+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+x)))); p} seq(n)={my(q=subst(B((n+1)\2), x, x^2), s=x^2+q^2/(1+q), p=x+O(x^2), t=p); for(n=1, n\2, t=x + q*(1 + p); p=x + x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2))) - t); Vec(p+t-x+O(x*x^n))} CROSSREFS Cf. A003430 (oriented), A339157, A339158, A339225 (unoriented). Sequence in context: A032173 A130616 A089324 * A297438 A111759 A305751 Adjacent sequences:  A339156 A339157 A339158 * A339160 A339161 A339162 KEYWORD nonn AUTHOR Andrew Howroyd, Nov 27 2020 STATUS approved

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)