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A092182
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Figurate numbers based on the 600-cell (4-D polytope with Schlaefli symbol {3,3,5}).
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7
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1, 120, 947, 3652, 9985, 22276, 43435, 76952, 126897, 197920, 295251, 424700, 592657, 806092, 1072555, 1400176, 1797665, 2274312, 2839987, 3505140, 4280801, 5178580, 6210667, 7389832, 8729425, 10243376, 11946195, 13852972, 15979377
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OFFSET
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1,2
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COMMENTS
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This is the 4-dimensional regular convex polytope called the 600-cell, hexacosichoron or hypericosahedron.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Hyun Kwang Kim, On Regular Polytope Numbers
Eric Weisstein's World of Mathematics, 600-Cell
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1). [From R. J. Mathar, Jun 21 2010]
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FORMULA
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a(n)=n*((145*n^3)-(280*n^2)+(179*n)-38)/6
a(n) = C(n+3,4) + 115 C(n+2,4) + 357 C(n+1,4) + 107 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+115*x+357*x^2+107*x^3)/(1-x)^5. [From R. J. Mathar, Jun 21 2010]
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EXAMPLE
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a(3)= 3*((145*3^3)-(280*3^2)+(179*3)-38)/6 = 3*(3915-2520+537-38)/6 = 0.5*1894 = 947
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PROG
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(MAGMA) [n*((145*n^3)-(280*n^2)+(179*n)-38)/6: n in [1..40]]; // Vincenzo Librandi, May 22 2011
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CROSSREFS
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Cf. A000332, A000583, A014820, A092181, A092183.
Sequence in context: A211471 A011245 A213875 * A133119 A052777 A052765
Adjacent sequences: A092179 A092180 A092181 * A092183 A092184 A092185
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KEYWORD
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easy,nonn
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AUTHOR
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Michael J. Welch (mjw1(AT)ntlworld.com), Mar 31 2004
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STATUS
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approved
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