|
Search: id:A089073
|
|
|
| A089073 |
|
Number of symmetric non-crossing connected graphs. |
|
+0
1
|
|
| 1, 1, 2, 5, 10, 32, 64, 231, 462, 1792, 3584, 14586, 29172, 122880, 245760, 1062347, 2124694, 9371648, 18743296, 84021990, 168043980, 763363328, 1526726656, 7012604550, 14025209100, 65028489216, 130056978432, 607892634420
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Number of symmetric non-crossing connected graphs on n equidistant nodes on a circle (it is assumed that the axis of symmetry is a diameter of the circle passing through a given node). Example: a(4)=5 because on the nodes A,B,C,D (axis of symmetry through A) the only symmetric non-crossing connected graphs are {AB,AC,AD), (AC,BC,DC), (AB,BC,CD,DA), (AB,BC,CD,DA,BD), (AB,BC,CD,DA,AC).
|
|
REFERENCES
|
P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 1999, 203-229.
|
|
FORMULA
|
a(2k)=4^k*binom((3k-1)/2, k)/[2(k+1)], a(2k+1)=2a(2k). a(2k)=(1/2)A078531(k), a(2k+1)=A078531(k).
|
|
MAPLE
|
a := proc(n) if n mod 2 = 0 then 4^(n/2)*binomial((3*(n/2)-1)/2, n/2)/2/(n/2+1) else 2*4^((n-1)/2)*binomial((3*((n-1)/2)-1)/2, (n-1)/2)/2/((n-1)/2+1) fi end;
|
|
CROSSREFS
|
Cf. A078531.
Adjacent sequences: A089070 A089071 A089072 this_sequence A089074 A089075 A089076
Sequence in context: A101957 A047113 A018386 this_sequence A138190 A056300 A018418
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 04 2003
|
|
|
Search completed in 0.002 seconds
|
