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A193253
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Great rhombicosidodecahedron with faces of centered polygons.
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1
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1, 183, 905, 2527, 5409, 9911, 16393, 25215, 36737, 51319, 69321, 91103, 117025, 147447, 182729, 223231, 269313, 321335, 379657, 444639, 516641, 596023, 683145, 778367, 882049, 994551, 1116233, 1247455, 1388577, 1539959, 1701961, 1874943, 2059265, 2255287
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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 great rhombicosidodecahedron. Each iteration requires the addition of n-2 edges and n-1 vertices to complete the centered polygon of each face.
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LINKS
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FORMULA
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a(n) = 60*n^3 - 90*n^2 + 32*n - 1.
G.f.: x*(1 + 179*x + 179*x^2 + x^3)/(1-x)^4 = x*(1+x)*(1 + 178*x + x^2)/(1-x)^4. - Colin Barker, Feb 12 2012
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {1, 183, 905, 2527}, 50] (* Vincenzo Librandi, Feb 18 2012 *)
a[n_]:=60*n^3 - 90*n^2 + 32*n - 1 ; Array[a, 50] (* or *)
CoefficientList[Series[(1 + x)*(1 + 178*x + x^2)/(1 - x)^4 , {x, 0, 50}], x] (* Stefano Spezia, Sep 02 2018 *)
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PROG
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(Excel) =60*ROW()^3-90*ROW()^2+32*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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