

A099129


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


2




OFFSET

1,2


COMMENTS



REFERENCES

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


LINKS



FORMULA

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



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



