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A339284
Number of unoriented series-parallel networks with integer valued elements summing to n.
0
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.
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 30 2020
STATUS
approved