

A099179


Iterated tetrahedral numbers, starting at Tet(2) = 4.


6




OFFSET

1,1


COMMENTS

The next term, a(8), has 228 digits.  Harvey P. Dale, Dec 18 2012


REFERENCES

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 83.
H. S. M. Coxeter, Polyhedral numbers, pp. 2535 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.


LINKS

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."


FORMULA

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(n1)).  R. J. Mathar, Jun 09 2008


EXAMPLE

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.


MATHEMATICA

NestList[(#(#+1)(#+2))/6&, 2, 6] (* Harvey P. Dale, Dec 18 2012 *)


CROSSREFS

Cf. A007501, A000292.
Sequence in context: A325503 A087314 A326972 * A102049 A058522 A292534
Adjacent sequences: A099176 A099177 A099178 * A099180 A099181 A099182


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 15 2004


EXTENSIONS

Corrected and extended by R. J. Mathar, Jun 09 2008


STATUS

approved



