A339291 Number of essentially series achiral series-parallel networks with n elements and without multiple unit elements in parallel.
0, 1, 1, 1, 2, 4, 6, 13, 21, 44, 76, 158, 281, 584, 1067, 2211, 4131, 8535, 16231, 33481, 64594, 133067, 259821, 534869, 1054751, 2170736, 4316320, 8884035, 17788985, 36627593, 73776883, 151996070, 307705669, 634411061, 1289890551, 2661708319
Offset: 1
Keywords
Examples
In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'. a(2) = 1: (oo). a(3) = 1: (ooo). a(4) = 1: (oooo). a(5) = 2: (ooooo), (o(o|oo)o). a(6) = 4: (oooooo), ((o|oo)(o|oo)), (o(o|ooo)o), (o(oo|oo)o).
Programs
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PARI
\\ here B(n) gives A339290 as a power series. EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} B(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = Z + (1 + Z)*x*Ser(EulerT( Vec(p^2/(1+p), -n) ))); p} seq(n, Z=x)={my(q=subst(B((n+1)\2, Z), x, x^2), s=q^2/(1+q), p=O(x^2)); forstep(n=2, n, 2, p=q*(1 + Z + (1 + Z)*x*Ser(EulerT(Vec(p+(s-subst(p, x, x^2))/2, 1-n))) - p)); Vec(p+O(x*x^n), -n)}
Comments