%I A099187
%S A099187 1,20,34220,180318314012420,
%T A099187 26383476911029432816173777932463879690054620,
%U A099187 8264348019814394793633513936351180099284347330550299669580038719038404485438240024692495732048618217524720985\
               1115982144818285080820
%N A099187 Iterated dodecahedral numbers, starting with Dod(2) = 20; a(1) = 20, 
               a(2) = Dod(a(1)) = Dod(20) = 34220; a(3) = Dod(34220)...
%C A099187 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.
%D A099187 H. S. M. Coxeter, "Regular Polytopes", New York: Dover, 1973.
%D A099187 J. V. Post, "Iterated Triangular Numbers", preprint.
%H A099187 H. K. Kim, <a href="http://com2mac.postech.ac.kr/papers/2001/01-22.pdf">
               On Regular Polytope Numbers</a>, as PDF file.
%H A099187 J. V. Post, <a href="http://magicdragon.com/poly.html">Table of Polytope 
               Numbers, Sorted, Through 1,000,000</a>.
%F A099187 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)).
%e A099187 a(2) = 34220 because a(0) = 1; a(1) = Dod(2) = the 2nd dodecahedral number 
               =
%e A099187 2*(9*2^2-9*2+2)/2 = 20; a(2) = Dod(Dod(2)) = the 20th dodecahedral number 
               =
%e A099187 20*(9*20^2-9*20+2)/2 = 34220.
%Y A099187 Cf. A007501, A006566.
%Y A099187 Sequence in context: A146497 A060618 A064487 this_sequence A129041 A129040 
               A159370
%Y A099187 Adjacent sequences: A099184 A099185 A099186 this_sequence A099188 A099189 
               A099190
%K A099187 easy,nonn,uned
%O A099187 0,2
%A A099187 Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 15 2004