|
Search: id:A114289
|
|
|
| A114289 |
|
Number of combinatorial types of n-dimensional polytopes with n+3 vertices. |
|
+0
3
|
|
| 0, 1, 7, 31, 116, 379, 1133, 3210, 8803, 23701, 63239, 168287, 447905, 1194814, 3196180, 8576505, 23081668, 62292381, 168536249, 457035453, 1241954405, 3381289332, 9221603416, 25189382006, 68906572413, 188750887991
(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:=60: with(numtheory): G:=-ln(1-2*x^3/(1-2*x)^2): H:=-ln(1-2*x)+ln(1-x): K:=-1/2*x*(x-8*x^3-1+5*x^2-7*x^4+2*x^6+5*x^8-9*x^7+19*x^5-14*x^9+x^10+19*x^11-5*x^12+4*x^14-8*x^13)/(1-x)^5/(2*x^6-4*x^4+4*x^2-1)/(x+1)^2: series(1/(x^3-x^4)*(1/4*sum(phi(2*r+1)/(2*r+1)*subs(x=x^(2*r+1), G), r=0..N)+1/2*sum(phi(r)/r*subs(x=x^r, H), r=1..N)+K), x, N);
|
|
CROSSREFS
|
Cf. A000943, A114290, A114291.
Sequence in context: A006458 A091344 A032197 this_sequence A048775 A125193 A002184
Adjacent sequences: A114286 A114287 A114288 this_sequence A114290 A114291 A114292
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Eric Fusy (eric.fusy(AT)inria.fr), Nov 21 2005
|
|
|
Search completed in 0.002 seconds
|
