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A099187
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Iterated dodecahedral numbers, starting with a(1) = 20.
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1
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OFFSET
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0,2
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COMMENTS
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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.
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REFERENCES
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H. S. M. Coxeter, "Regular Polytopes", New York: Dover, 1973.
J. V. Post, "Iterated Triangular Numbers", preprint.
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LINKS
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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.
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FORMULA
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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)).
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A007501, A006566.
Sequence in context: A348144 A060618 A064487 * A129041 A129040 A159370
Adjacent sequences: A099184 A099185 A099186 * A099188 A099189 A099190
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Nov 15 2004
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STATUS
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approved
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