|
Search: id:A114290
|
|
|
| A114290 |
|
Number of oriented n-dimensional polytopes with n+3 vertices, meaning that two polytopes are identified if they have the same combinatorial type and there exists an orientation-preserving homeomorphism mapping the first polytope to the second polytope. |
|
+0
3
|
|
| 0, 1, 7, 38, 170, 617, 1979, 5859, 16571, 45516, 123159, 330736, 885780, 2372305, 6362965, 17102719, 46078541, 124440388, 336829857, 913658780, 2483217288, 6761405513, 18441239903, 50375429081, 137807555515, 377492301876
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
REFERENCES
|
\'E. Fusy, Counting d-polytopes with d+3 vertices, http://arXiv.org/abs/math.CO/0511466
B. Gr{\"u}nbaum, Convex Polytopes, Springer-Verlag, 2003, Second edition prepared by V. Kaibel, V. Klee and G. M. Ziegler, p. 121a.
E. K. Lloyd, The number of d-polytopes with d+3 vertices, Mathematika 17 (1970), 120-132.
|
|
MAPLE
|
N:=30: with(numtheory): G:=-ln(1-2*x^3/(1-2*x)^2): H:=-log(1-2*x)+ln(1-x): K:=-(x^10+3*x^9-3*x^8-7*x^7+4*x^6+4*x^5+4*x^4+3*x^3-2*x^2+1)*x/(1-x)^5/(x+1)^3: series(1/(x^3-x^4)*(1/2*sum(phi(2*r+1)/(2*r+1)*subs(x=x^(2*r+1), G), r=0..N)+sum(phi(r)/r*subs(x=x^r, H), r=1..N)+K), x, N);
|
|
CROSSREFS
|
Cf. A000943, A114289, A114291.
Sequence in context: A129736 A003352 A034858 this_sequence A000531 A099453 A026763
Adjacent sequences: A114287 A114288 A114289 this_sequence A114291 A114292 A114293
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Eric Fusy (eric.fusy(AT)inria.fr), Nov 21 2005
|
|
|
Search completed in 0.002 seconds
|
