|
Search: id:A001677
|
|
|
| A001677 |
|
Number of series-parallel networks with n edges.
(Formerly M0797 N0302)
|
|
+0
2
|
|
| 1, 2, 3, 6, 12, 26, 59, 146, 368, 976, 2667, 7482, 21440, 62622, 185637, 557680, 1694256, 5198142, 16086486, 50165218, 157510504, 497607008, 1580800091, 5047337994, 16190223624, 52153429218, 168657986843, 547389492416
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
REFERENCES
|
R. M. Foster, The number of series-parallel networks, Proc. Intern. Congr. Math., Vol. 1, 1960, p. 646.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
B. D. H. Tellegen, Geometrical configurations and duality of electrical networks, Philips Technical Review, 5 (1940), 324-330.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=2..500
|
|
FORMULA
|
a(n) = s(n) - (1/2)*Sum_{i=1..n-1} s(i)*s(n-i) - (1/2)*s(n/2), where s() = A000084 and the last rerm is omitted if n is odd.
|
|
EXAMPLE
|
a(5) = 24 - (1/2)*(1*10+2*4+4*2+10*1) = 6.
|
|
CROSSREFS
|
Cf. A058642, A058668.
Sequence in context: A151527 A086625 A152172 this_sequence A024422 A019525 A108915
Adjacent sequences: A001674 A001675 A001676 this_sequence A001678 A001679 A001680
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 20 2000
|
|
|
Search completed in 0.002 seconds
|
