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

0,3

Comments

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

Links

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

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

Example

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.

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 *)

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), A097547.

Sequence in context: A286314 A099124 A172862 * A286392 A221926 A324232

Adjacent sequences: A099126 A099127 A099128 * A099130 A099131 A099132

Keyword

nonn,easy

Author

Jonathan Vos Post, Nov 14 2004

Extensions

Offset changed to 1 by Georg Fischer, Jun 20 2022

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

Status

approved