Search: id:A099187 Results 1-1 of 1 results found. %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, On Regular Polytope Numbers, as PDF file. %H A099187 J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000. %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 Search completed in 0.001 seconds