

A099129


Let T(n) be the nth triangular number n*(n+1)/2; then a(n) = nth iteration T(T(T(...(n)))).


2




OFFSET

0,2


COMMENTS

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


REFERENCES

J. V. Post, "Iterated Triangular Numbers", preprint.
J. V. Post, "Iterated Polygonal Numbers", preprint.


LINKS

Table of n, a(n) for n=0..6.


FORMULA

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


EXAMPLE

a(3) = 231 because we can write the 3time iterated expression on T(3), the triangular number sequence n*(n+1)/2, namely: T(T(T(3))) = 231.


MATHEMATICA

Table[Nest[(#(#+1))/2&, n, n], {n, 8}] (* Harvey P. Dale, May 29 2013 *)


PROG

(PARI) a(n) = my(k = n); for (j=1, n, k = k*(k+1)/2; ); k; \\ Michel Marcus, Jan 01 2017


CROSSREFS

Cf. A000217, A007501, A058009 (analog with primes).
Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232
Adjacent sequences: A099126 A099127 A099128 * A099130 A099131 A099132


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Nov 14 2004


STATUS

approved



