cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A339284 #5 Nov 30 2020 21:40:24
%S A339284 1,3,7,23,73,281,1112,4779,21139,96793,451631,2144101,10303984,
%T A339284 50042734,245110900,1209414659,6005130171,29983077169,150437143336,
%U A339284 758110844897,3835445581758,19473373629628,99189996107004,506726776334889,2595687705113097
%N A339284 Number of unoriented series-parallel networks with integer valued elements summing to n.
%C A339284 See A339282 for additional details.
%e A339284 In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'.
%e A339284 a(1) = 1: (1).
%e A339284 a(2) = 3: (2), (11), (1|1).
%e A339284 a(3) = 7: (3), (12), (1(1|1)), (111), (1|2), (1|11), (1|1|1).
%o A339284 (PARI)
%o A339284 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A339284 B(n, Z)={my(p=Z+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); p}
%o A339284 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}
%o A339284 seq(n)={EdgeWeightedT(vector(n,i,1))}
%Y A339284 Cf. A339225, A339230, A339282, A339283.
%K A339284 nonn
%O A339284 1,2
%A A339284 _Andrew Howroyd_, Nov 30 2020