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A099179 Iterated tetrahedral numbers, starting at Tet(2) = 4. 6
2, 4, 20, 1540, 609896980, 37811003218473324699257860, 9009555207802177724984164589516456320805205201729086740415363658290866918420 (list; graph; refs; listen; history; text; internal format)
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. 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.

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(n-1)). - 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

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)