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Search: id:A114291
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| A114291 |
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Number of combinatorial types of achiral n-dimensional polytopes with n+3 vertices, where a polytope is achiral if one of its geometric realizations has a reflection-symmetry. |
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+0
3
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| 0, 1, 7, 24, 62, 141, 287, 561, 1035, 1886, 3319, 5838, 10030, 17323, 29395, 50291, 84795, 144374, 242641, 412126, 691522, 1173151, 1966929, 3334931, 5589311, 9474106, 15875699, 26906538, 45083426, 76404103, 128014623, 216944163
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OFFSET
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1,3
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REFERENCES
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\'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.
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FORMULA
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G.f.: A(x)=(2*x^11+4*x^10-2*x^9-15*x^8-5*x^7+23*x^6+15*x^5-17*x^4-14*x^3+4*x^2+5*x+1)*x^2/(-1+x)^5/(2*x^6-4*x^4+4*x^2-1)/(x+1)^3.
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CROSSREFS
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Cf. A000943, A114289, A114290.
Sequence in context: A062449 A014205 A029585 this_sequence A101903 A050191 A021000
Adjacent sequences: A114288 A114289 A114290 this_sequence A114292 A114293 A114294
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KEYWORD
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nonn
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AUTHOR
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Eric Fusy (eric.fusy(AT)inria.fr), Nov 21 2005
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