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A193252
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Great rhombicuboctahedron with faces of centered polygons.
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2
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1, 75, 365, 1015, 2169, 3971, 6565, 10095, 14705, 20539, 27741, 36455, 46825, 58995, 73109, 89311, 107745, 128555, 151885, 177879, 206681, 238435, 273285, 311375, 352849, 397851, 446525, 499015, 555465, 616019, 680821, 750015, 823745, 902155, 985389, 1073591
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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) edge units and (n-1) vertices to complete the centered polygon of each face: centered squares, centered octagons and centered hexagons.
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LINKS
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FORMULA
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a(n) = 24*n^3 - 36*n^2 + 14*n - 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=75, a(2)=365, a(3)=1015. - Harvey P. Dale, Jul 27 2011
E.g.f.: 1 + (-1 + 2*x + 36*x^2 + 24*x^3)*exp(x). - G. C. Greubel, Feb 26 2019
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MATHEMATICA
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Table[24n^3-36n^2+14n-1, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 75, 365, 1015}, 40] (* Harvey P. Dale, Jul 27 2011 *)
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PROG
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(Excel) =24*ROW()^3-36*ROW()^2+14*ROW()-1
(PARI) for(n=1, 40, print1(24*n^3-36*n^2+14*n-1", ")); \\ Bruno Berselli, Jul 21 2011
(Sage) [24*n^3 -36*n^2 +14*n -1 for n in (1..40)] # G. C. Greubel, Feb 26 2019
(GAP) List([1..40], n-> 24*n^3 -36*n^2 +14*n -1) # G. C. Greubel, Feb 26 2019
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CROSSREFS
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Cf. A001844 (centered square numbers), A016754 (centered octagonal numbers), A003215 (centered hexagonal numbers).
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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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