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A193251
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Small rhombicosidodecahedron with faces of centered polygons.
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1
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1, 123, 605, 1687, 3609, 6611, 10933, 16815, 24497, 34219, 46221, 60743, 78025, 98307, 121829, 148831, 179553, 214235, 253117, 296439, 344441, 397363, 455445, 518927, 588049, 663051, 744173, 831655, 925737, 1026659, 1134661, 1249983, 1372865, 1503547
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OFFSET
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1,2
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COMMENTS
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The sequence starts with a central dot and expands outward with (n-1) centered polygonal pyramids producing a small rhombicosidodecahedron. Each iteration requires the addition of (n-2) edges and (n-1) vertices to complete the centered polygon of each face. [centered triangles (A005448), centered squares (A001844) and centered pentagons (A005891) ]
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LINKS
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FORMULA
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a(n) = 40*n^3 - 60*n^2 + 22*n - 1.
G.f.: x*(1+x)*(x^2 + 118*x + 1) / (x-1)^4. - R. J. Mathar, Aug 26 2011
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PROG
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(Excel) copy and paste the formula =40 *ROW()^3-60 *ROW()^2+22*ROW()-1 fill down to desired size.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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