login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099187 Iterated dodecahedral numbers, starting with a(1) = 20. 1
1, 20, 34220, 180318314012420, 26383476911029432816173777932463879690054620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This need not start with Dod(2) = 20. For example, if a(1) = Dod(3) = 84, then a(2) = Dod(Dod(3)) = Dod(84) = 84*(9*84^2 - 9*84 + 2)/2 = 2635500; a(3) = Dod(Dod(Dod(3))) = Dod(2635500) = 82376134843569010500. The core sequence is not to be confused with Rhombic dodecahedral numbers.

REFERENCES

H. S. M. Coxeter, "Regular Polytopes", New York: Dover, 1973.

J. V. Post, "Iterated Triangular Numbers", preprint.

LINKS

Michel Marcus, Table of n, a(n) for n = 0..6

Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.

FORMULA

From the definition of dodecahedral numbers, for n>1, Dod(n) = n*(9*n^2-9*n+2)/2 we have a(0) = 1, a(1) = Dod(2) = 20; a(k+1) = Dod(a(k)).

EXAMPLE

a(0) = 1;

a(1) = Dod(2) = the 2nd dodecahedral number = 2*(9*2^2-9*2+2)/2 = 20;

a(2) = Dod(Dod(2)) = the 20th dodecahedral number = 20*(9*20^2-9*20+2)/2 = 34220.

MATHEMATICA

Dod[n_]:= n*(9*n^2-9*n+2)/2; a[n_]:= If[n==0, Dod[1], If[n==1, Dod[2], Dod[a[n-1]]]]; Table[a[n], {n, 0, 4}] (* G. C. Greubel, Mar 22 2019 *)

PROG

(PARI) dod(n) = n*(9*n^2-9*n+2)/2;

a(n) = if (n==0, 1, if (n==1, dod(2), dod(a(n-1)))); \\ Michel Marcus, Dec 14 2015

CROSSREFS

Cf. A007501, A006566.

Sequence in context: A146497 A060618 A064487 * A129041 A129040 A159370

Adjacent sequences:  A099184 A099185 A099186 * A099188 A099189 A099190

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 15 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)