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A099129
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Let T(n) be the n-th triangular number n*(n+1)/2; then a(n) = n-th iteration T(T(T(...(n)))).
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2
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OFFSET
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0,2
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COMMENTS
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The growth of this sequence is faster than exponential. This can be derived from the exponential generating function for triangular numbers: g(x) = (1 + 2x + x^2/2)*e^x = 1 + 3x/1! + 6x^2/2! + 10x^3/3! + 15x^4/4! + 21x^5/5! + ...
The next term, a(8), has 162 digits. - Harvey P. Dale, May 29 2013
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REFERENCES
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J. V. Post, "Iterated Triangular Numbers", preprint.
J. V. Post, "Iterated Polygonal Numbers", preprint.
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LINKS
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Table of n, a(n) for n=0..6.
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FORMULA
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a(n) = A007501(n, n)
The sequence grows like O(n^2^n*1/2^n). This can be derived from the growth O(n^2*1/2) of the triangle sum by iteration. - Hieronymus Fischer, Jan 21 2006
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EXAMPLE
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a(3) = 231 because we can write the 3-time iterated expression on T(3), the triangular number sequence n*(n+1)/2, namely: T(T(T(3))) = 231.
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MATHEMATICA
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Table[Nest[(#(#+1))/2&, n, n], {n, 8}] (* Harvey P. Dale, May 29 2013 *)
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PROG
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(PARI) a(n) = my(k = n); for (j=1, n, k = k*(k+1)/2; ); k; \\ Michel Marcus, Jan 01 2017
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CROSSREFS
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Cf. A000217, A007501, A058009 (analog with primes).
Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232
Adjacent sequences: A099126 A099127 A099128 * A099130 A099131 A099132
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Nov 14 2004
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STATUS
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approved
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