A339284 Number of unoriented series-parallel networks with integer valued elements summing to n.

1, 3, 7, 23, 73, 281, 1112, 4779, 21139, 96793, 451631, 2144101, 10303984, 50042734, 245110900, 1209414659, 6005130171, 29983077169, 150437143336, 758110844897, 3835445581758, 19473373629628, 99189996107004, 506726776334889, 2595687705113097

Offset

1,2

Comments

See A339282 for additional details.

Links

Table of n, a(n) for n=1..25.

Example

In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'.
a(1) = 1: (1).
a(2) = 3: (2), (11), (1|1).
a(3) = 7: (3), (12), (1(1|1)), (111), (1|2), (1|11), (1|1|1).

Prog

(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
B(n, Z)={my(p=Z+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); p}
EdgeWeightedT(u)={my(Z=x*Ser(u), n=#u, q=subst(B((n+1)\2, Z), x, x^2), s=subst(Z, x, x^2)+q^2/(1+q), p=Z+O(x^2), t=p); for(n=1, n\2, t=Z + q*(1 + p); p=Z + x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2))) - t); Vec(p+t-Z+B(n, Z))/2}
seq(n)={EdgeWeightedT(vector(n, i, 1))}

Crossrefs

Cf. A339225, A339230, A339282, A339283.

Sequence in context: A191638 A148704 A283109 * A057184 A148705 A148706

Adjacent sequences: A339281 A339282 A339283 * A339285 A339286 A339287

Keyword

nonn

Author

Andrew Howroyd, Nov 30 2020

Status

approved