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A099179
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Iterated tetrahedral numbers, starting at Tet(2) = 4.
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6
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OFFSET
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1,1
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COMMENTS
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The next term, a(8), has 228 digits. - Harvey P. Dale, Dec 18 2012
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 83.
H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.
J. V. Post, "Iterated Triangular Numbers", preprint.
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LINKS
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Table of n, a(n) for n=1..7.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000
Eric Weisstein's World of Mathematics, "Tetrahedral Number."
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FORMULA
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Given the tetrahedral number formula Tet(n) = n*(n+1)*(n+2)/6, define a(1) = 2; a(2) = the 2nd tetrahedral number = 2*(2+1)*(2+2)/6 = 4; Define a(k+1) = Tet(a(k)) = a(k)*[a(k)+1]*[a(k)+2]/6.
a(n)= A000292(a(n-1)). - R. J. Mathar, Jun 09 2008
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EXAMPLE
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a(2) = Tet(2) = the 2nd tetrahedral number = 2*(2+1)*(2+2)/6 = 4;
a(3) = Tet(Tet(2)) = the 4th tetrahedral number = 4*(4+1)*(4+2)/6 = 20;
a(4) = Tet(Tet(Tet(2))) = the 20th tetrahedral number = 20*(20+1)*(20+2)/6 = 1540.
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MATHEMATICA
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NestList[(#(#+1)(#+2))/6&, 2, 6] (* Harvey P. Dale, Dec 18 2012 *)
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CROSSREFS
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Cf. A007501, A000292.
Sequence in context: A059588 A132498 A087314 * A102049 A058522 A122736
Adjacent sequences: A099176 A099177 A099178 * A099180 A099181 A099182
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Nov 15 2004
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EXTENSIONS
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Corrected and extended by R. J. Mathar, Jun 09 2008
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STATUS
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approved
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