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A339223 Number of essentially series unoriented series-parallel networks with n elements. 3
1, 1, 2, 6, 17, 57, 196, 723, 2729, 10638, 42161, 169912, 692703, 2853523, 11852644, 49592966, 208800209, 883970867, 3760605627, 16068272965, 68925340187, 296705390322, 1281351319402, 5549911448062, 24103086681839, 104938476264310, 457920147387969, 2002462084788769 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A339225 for additional details.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

a(n) = (A007453(n) + A339157(n))/2.

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) = 1: (oo), (o|o).

a(3) = 2: (ooo), (o(o|o)).

a(4) = 6: (oooo), (oo(o|o)), (o(o|o)o), ((o|o)(o|o)), (o(o|oo)), (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)); for(n=1, n\2, p = x + q*(1 + x + x*Ser(EulerT(Vec(p+(s-subst(p, x, x^2))/2))) - p)); Vec(p+x+subst(x^2/(1+x), x, B(n)))/2}

CROSSREFS

Cf. A003430, A007453 (oriented), A339157 (achiral), A339224, A339225.

Sequence in context: A238127 A190915 A032132 * A148454 A007743 A000687

Adjacent sequences:  A339220 A339221 A339222 * A339224 A339225 A339226

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Nov 27 2020

STATUS

approved

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)