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A092181
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Figurate numbers based on the 24-cell (4-D polytope with Schlaefli symbol {3,4,3}).
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7
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1, 24, 153, 544, 1425, 3096, 5929, 10368, 16929, 26200, 38841, 55584, 77233, 104664, 138825, 180736, 231489, 292248, 364249, 448800, 547281, 661144, 791913, 941184, 1110625, 1301976, 1517049, 1757728, 2025969, 2323800, 2653321, 3016704
(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 24-cell, hyperdiamond or icositetrachoron.
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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, 24-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^2*((3*n^2)-(4*n)+2)
a(n) = C(n+3,4) + 19 C(n+2,4) + 43 C(n+1,4) + 9 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+19*x+43*x^2+9*x^3)/(1-x)^5. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2010]
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EXAMPLE
| a(3)= 3^2*((3*3^2)-(4*3)+2) = 9*(27-12+2) = 9*17 = 153
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PROG
| (MAGMA) [n^2*((3*n^2)-(4*n)+2): n in [1..40]]; // Vincenzo Librandi, May 22 2011
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CROSSREFS
| Cf. A000332, A000583, A014820, A092182, A092183.
Sequence in context: A042118 A039494 A159650 * A001702 A004308 A008663
Adjacent sequences: A092178 A092179 A092180 * A092182 A092183 A092184
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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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