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A058385
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Essentially parallel series-parallel networks with n unlabeled edges, multiple edges not allowed.
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3
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0, 1, 0, 1, 2, 4, 9, 20, 47, 112, 274, 678, 1709, 4346, 11176, 28966, 75656, 198814, 525496, 1395758, 3723986, 9975314, 26817655, 72332320, 195679137, 530814386, 1443556739, 3934880554, 10748839215, 29420919456, 80678144437, 221618678694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence q_n).
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LINKS
| Index entries for sequences mentioned in Moon (1987)
S. R. Finch, Series-parallel networks
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FORMULA
| G.f. satisfies 1-x+x^2+2*A(x) = Product_{j=1..inf} (1-x^j)^(-a(j)).
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MAPLE
| Q := x; q[1] := 1; for d from 1 to 40 do q[d+1] := c; Q := Q+c*x^(d+1); t0 := mul((1-x^j)^(-q[j]), j=1..d+1); t01 := series(t0, x, d+2); t05 := series(2*Q +1-x+x^2 -t01, x, d+2); t1 := coeff(t05, x, d+1); t2 := solve(t1, c); q[d+1] := t2; Q := subs(c=t2, Q); Q := series(Q, x, d+2); od: A058385 := n->coeff(Q, x, n);
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MATHEMATICA
| max = 31; f[x_] := Sum[a[k]*x^k, {k, 0, max}]; a[0] = 0; a[1] = 1; a[2] = 0; a[3] = 1; se = Series[ 1 - x + x^2 + 2*f[x] - Product[(1 - x^j)^(-a[j]), {j, 1, max}], {x, 0, max}]; sol = Solve[ Thread[ CoefficientList[ se, x] == 0]]; A058385 = Table[a[n], {n, 0, max}] /. First[sol] (* From Jean-François Alcover, Dec 27 2011, after g.f. *)
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CROSSREFS
| Cf. A058379, A058386, A058387.
Sequence in context: A196244 A035084 * A058386 A095980 A036619 A036620
Adjacent sequences: A058382 A058383 A058384 * A058386 A058387 A058388
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 20 2000
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