|
Search: id:A058379
|
|
|
| A058379 |
|
Essentially parallel series-parallel networks with n labeled edges, multiple edges not allowed. |
|
+0
9
|
|
| 0, 1, 0, 3, 7, 90, 676, 9058, 117286, 1934068, 34354196, 698971944, 15520697072, 379690093016, 10064445063128, 288507479108384, 8875736500909216, 291965748820524000, 10221371162528667136, 379535362671828005536, 14896748155197456096736
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
REFERENCES
|
J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence Q_n).
|
|
LINKS
|
Index entries for sequences mentioned in Moon (1987)
S. R. Finch, Series-parallel networks
|
|
FORMULA
|
E.g.f. satisfies A(x) = x + O(x^2), 2*A(x) = exp(A(x)) - 1 + log(1+x).
|
|
EXAMPLE
|
A(x) = x + 1/2*x^3 + 7/24*x^4 + 3/4*x^5 + 169/180*x^6 + ...
For n=4 there are two unlabeled networks:
..o.....o--o
./.\.../....\
o...o o------o
.\./
..o
which can be labeled in 3 (resp. 4) ways, for a total of 7.
|
|
MAPLE
|
Q := x; for d from 1 to 30 do Q := Q+c*x^(d+1)/(d+1)!; t1 := coeff(series(2*Q - (exp(Q)-1+log(1+x)), x, d+2), x, d+1); t2 := solve(t1, c); Q := subs(c=t2, Q); Q := series(Q, x, d+2); od: A058379 := n->coeff(Q, x, n)*n!; # method 1
Order := 50; t1 := solve(series((exp(A)-2*A-1), A)=-log(1+x), A); A058379 := n-> n!*coeff(t1, x, n); # method 2
|
|
CROSSREFS
|
Cf. A058380, A058381. See A000669 for unlabeled case when parallel edges are allowed.
Sequence in context: A082715 A041705 A137130 this_sequence A111002 A042481 A088419
Adjacent sequences: A058376 A058377 A058378 this_sequence A058380 A058381 A058382
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
njas, Dec 19 2000
|
|
|
Search completed in 0.002 seconds
|
