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Search: id:A099187
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| A099187 |
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Iterated dodecahedral numbers, starting with Dod(2) = 20; a(1) = 20, a(2) = Dod(a(1)) = Dod(20) = 34220; a(3) = Dod(34220)... |
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1
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| 1, 20, 34220, 180318314012420, 26383476911029432816173777932463879690054620, 82643480198143947936335139363511800992843473305502996695800387190384044854382400\ 246924957320486182175247209851115982144818285080820
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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H. K. Kim, On Regular Polytope Numbers, as PDF file.
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(2) = 34220 because 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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CROSSREFS
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Cf. A007501, A006566.
Sequence in context: A146497 A060618 A064487 this_sequence A129041 A129040 A159370
Adjacent sequences: A099184 A099185 A099186 this_sequence A099188 A099189 A099190
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 15 2004
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