A099129 Let T(n) be the n-th triangular number n*(n+1)/2; then a(n) = n-th iteration T(T(T(...(n)))).

0, 1, 6, 231, 1186570, 347357071281165, 2076895351339769460477611370186681, 143892868802856286225154411591351342616163027795335641150249224655238508171

Offset: 0

Author

Jonathan Vos Post, Nov 14 2004

Keywords

• nonn
• easy

Comments

The next term, a(8), has 162 digits. - Harvey P. Dale, May 29 2013

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A000217, A007501, A058009 (analog with primes), A097547.

Programs

Maple

a:= n-> (t-> (t@@n)(n))(j-> j*(j+1)/2):
seq(a(n), n=0..7);  # Alois P. Heinz, Sep 29 2023

Mathematica

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

PARI

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

Formula

a(n) = A000217^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

Extensions

Offset changed to 1 by Georg Fischer, Jun 20 2022

a(0)=0 prepended by Alois P. Heinz, Sep 29 2023