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Search: id:A130896
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| A130896 |
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For D_n type groups as polyhedra that are pyramid-like: {F,V,E,dimension}->{2*n+1,2*n+1,2*n,(2*n+1)*((2*n+1)-1)/2} such that Euler's equation is true: V=E-F+2. |
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| 3, 3, 4, 3, 5, 5, 8, 10, 7, 7, 12, 21, 9, 9, 16, 36, 11, 11, 20, 55, 13, 13, 24, 78, 15, 15, 28, 105, 17, 17, 32, 136, 19, 19, 36, 171, 21, 21, 40, 210, 23, 23, 44, 253, 25, 25, 48, 300, 27, 27, 52, 351, 29, 29, 56, 406, 31, 31, 60, 465, 33, 33, 64, 528, 35, 35, 68, 595, 37, 37
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This idea comes from the Octahedron being truncated by one vertex to give a pyramid. In this case the n=1 is not a 3d polyhedron, but the rest are very simple F=E figures. Adding one vertex below the plane of the major polygon gives an D_nh type point group ( D_n like figures A131498): these figures are Point groups C_nv.
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REFERENCES
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David M. Bishop, Group Theory and Chemistry,Dover Publications, 1993, table 3-7.1, page 46
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FORMULA
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{a(n),a(n+1),a(n+2),a(n+3) = {2*m+1,2*m+1,4*m,(2*m+1)*((2*m+1)-1)/2}: m=Floor[n/4]
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MATHEMATICA
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a = Table[{2*n + 1, 2*n + 1, 4*n, (2*n + 1)*((2*n + 1) - 1)/2}, {n, 1, 32}]; Flatten[a]
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CROSSREFS
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Cf. A131498.
Sequence in context: A096139 A123708 A102302 this_sequence A029882 A083503 A062069
Adjacent sequences: A130893 A130894 A130895 this_sequence A130897 A130898 A130899
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 22 2007
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