|
Search: id:A133189
|
|
|
| A133189 |
|
Number of simple directed graphs on n labeled nodes consisting only of some cycle graphs C_2 and nodes not part of a cycle having directed edges to both nodes in exactly one cycle. |
|
+0
3
|
|
| 1, 0, 1, 3, 9, 40, 210, 1176, 7273, 49932, 372060, 2971540, 25359411, 230364498, 2215550428, 22460391240, 239236043985, 2669869110856, 31134833803728, 378485082644400, 4786085290280275, 62838103267148790, 855122923978737876
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
REFERENCES
|
A. P. Heinz (1990). Analyse der Grenzen und Moeglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universitaet Freiburg, Freiburg i. Br., Germany.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
a(n) = sum_{k=0..floor(n/2)} (binomial (n, 2k) * A006882(2k-1) * k^(n-2k)).
|
|
EXAMPLE
|
a(3)=3, because there are 3 graphs of the given kind for 3 labeled nodes: 3->1<->2<-3; 2->1<->3<-2; 1->2<->3<-1;
|
|
MAPLE
|
A006882:= proc(n) option remember; if n<=1 then 1 else n*A006882(n-2); fi; end; a:= proc(n) option remember; add (binomial (n, k+k) *A006882(k+k-1) *k^(n-k-k), k=0..floor(n/2)); end; seq (a(n), n=0..30);
|
|
CROSSREFS
|
Cf. A006882, A007318, A135458, A135429.
Sequence in context: A079096 A143293 A101395 this_sequence A020092 A027893 A018417
Adjacent sequences: A133186 A133187 A133188 this_sequence A133190 A133191 A133192
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Dec 17 2007
|
|
|
Search completed in 0.002 seconds
|
