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A092183
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Figurate numbers based on the 120-cell (4-D polytope with Schlaefli symbol {5,3,3}).
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7
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1, 600, 4983, 19468, 53505, 119676, 233695, 414408, 683793, 1066960, 1592151, 2290740, 3197233, 4349268, 5787615, 7556176, 9701985, 12275208, 15329143, 18920220, 23108001, 27955180, 33527583, 39894168, 47127025, 55301376
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the 4-dimensional regular convex polytope called the 120-cell, hecatonicosachoron or hyperdodecahedron.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Hyun Kwang Kim, On Regular Polytope Numbers.
Eric Weisstein's World of Mathematics, 120-Cell
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2010]
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FORMULA
| a(n)=n*((261*n^3)-(504*n^2)+(283*n)-38)/2
a(n) = C(n+3,4) + 595 C(n+2,4) + 1993 C(n+1,4) + 543 C(n,4)
a(n)= +5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5). G.f.: x*(1+595*x+1993*x^2+543*x^3)/(1-x)^5. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2010]
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EXAMPLE
| a(3)=3*((261*3^3)-(504*3^2)+(283*3)-38)/2 = 3*(7047-4536+849-38)/2 = 1.5*3322 = 4983
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PROG
| (MAGMA) [n*((261*n^3)-(504*n^2)+(283*n)-38)/2: n in [1..40]]; // Vincenzo Librandi, May 22 2011
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CROSSREFS
| Cf. A000332, A000583, A014820, A092181, A092182.
Sequence in context: A172244 A090222 A157918 * A048530 A023915 A035850
Adjacent sequences: A092180 A092181 A092182 * A092184 A092185 A092186
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KEYWORD
| easy,nonn
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AUTHOR
| Michael J. Welch (mjw1(AT)ntlworld.com), Mar 31 2004
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