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 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, If[n==1, Dod, 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

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